The proofs of Theorem 1-3 are along the lines of Wied and Galeano (2013).
|
|
- Thomasine Moody
- 6 years ago
- Views:
Transcription
1 A Appendix: Proofs The proofs of Theore 1-3 are along the lines of Wied and Galeano (2013) Proof of Theore 1 Let D[d 1, d 2 ] be the space of càdlàg functions on the interval [d 1, d 2 ] equipped with the supreu nor Denote the tie invariant vector of variances by σ 2 = ( σ 2 1,, σ2 p) and define {P (d), d [c, B]} by P (d) = ˆD 1 2 [ d] [ c] ([ ] ) ˆσ 2 [ d] [ c] σ2 = ˆD [ d] [ c] 2 1 [ ] [ d] ˆσ 2 1 [ c] σ2 1 [ ] [ d] ˆσ 2 p [ c] σ2 p To obtain convergence on D[c, B], we use the invariance principle of Theore 2918 in Davidson (1994) and argue analogously to Lea A1 in Wied et al (2012b) For fixed c 0 and assuing, {P (d), d [c, B]} converges in distribution to {W p (d) W p (c), d [c, B]} with W p ( ) being a p diensional Brownian Motion S (b) := ˆD 1 2 [ b]+2 ([ ] ) +[ b]+2 ˆσ 2 σ 2 +1 ([ ˆD ] 1 2 ˆσ 2 σ2) 1 d W p (b + 1) W p (1), for b [0, B] W p (1) Consequently, V [ b]+2 = ˆD 1 2 [ b] + 2 ([ ] ) ˆσ 2 +[ b]+2 σ 2 ˆD [ b] + 2 ([ ˆσ 2 ] 1 σ2) converges to the process {W p (b+1) (b+1)w p (1), b [0, B]} Applying the continuous apping theore and calculating the covariance structure of the liit process proves the result Proof of Theore 2 The proof uses the sae arguents as the one of Theore 1 and is ainly based on the fact 1
2 that for fixed c 0, and the process {P (d), d [c, B]} converges in distribution to W p (d) W p (c) + H d c d c g 1(z)dz, d [c, B] g p(z)dz on D[c, B] The constant H is, up to a constant, the liit of ˆD under the null hypothesis, see the proof of Theore 2 in Wied et al (2012a) This result is a generalization of arguents used in Theore 2 in Wied et al (2012a), executed along the lines of to the proof of Theore 1 Proof of Theore 3 Assue wlog g 1 ( ) Mh( ) Then, the detector converges in the following way: sup b [0,B] V 2 b +2 M b+1 h(u)du 1 G d 1 (b) b+1 sup g b [0,B] + D (u)du 2 (1) G p (b) b+1 g p (u)du 1 2 Denote D 1 2 ( di j ) and define constants c 1(b) b+1 i, j=1,,p 1 i = 2,, p Thus, (1) has asyptotically the sae distribution as h(u)du and c i (b) b+1 g 1 i (u)du, sup b [0,B] p G j(b) + Md j1 c 1 (b) + j=1 2 p d ji c i (b) (2) i=2 Since D p is positive definite there exists j {1,, p} with d j1 0 Assuing M, we have G j (b) + Md j1 c 1 (b) p Thus, Jensen s inequality iplies that for all b (0, B] the square root of the su in (2) tends to The fact that the ter degenerates for b = 0 does not affect this result, since this event occurs with zero probability This iplies that (2) will exceed every quantile of the asyptotic null distribution for M 2
3 Proof of Lea 1 Hafner (2003) provides conditions to establish the existence of the atrix of fourth oents and cross oents of a ultivariate GARCH(1, 1) odel in vech representation: vech (H t ) = C 0 + A 1 vech ( X t 1 X t 1) + B1 vech (H t 1 ), (3) where C 0 is a d diensional paraeter vector and A 1 and B 1 are paraeter atrices of diension d d The closely related vec representation is given as vec (H t ) = C 0 + A 1 vec ( X t 1 X ) t 1 + B 1 vec (H t 1) (4) and contains several redundant equations that lead to inflated paraeter atrices A 1 and B 1 of diension p 2 p 2 and a paraeter vector C 0 of diension p2 Following Engle and Kroner (1995), the odel in (7) in the ain paper can be given in vec representation by choosing C 0 = (1 α β) [ H 1 2 H 1 2 ] vec ( Ip ), A 1 = αi p 2 and B 1 = βi p2 (5) in (4) Thus, (7) can be given in vech representation by transforing it first to its vec and then to its vech representation Substituting (5) in (4) and ultiplying D p and L p gives C 0 = (1 α β) L p H 1 2 H 1 2 vec ( Ip ), A1 = αi d and B 1 = βi d (6) in odel (3) Note that A 1 A 1 = α 2 I d 2, B 1 B 1 = β 2 I d 2 and A 1 B 1 = B 1 A 1 = αβi d 2 Using (6) and G p fro Hafner (2003) to construct Z allows to check the existence of Γ according to Hafner (2003) 3
4 B Appendix: Further Siulations: Monitoring Tie Series of IID Rando Vectors To begin with, we investigate the size of the proposed procedure under the null hypothesis of no structural break First, we siulate tie series that capture neither serial nor cross-sectional dependence to gain reference values to which the perforance in ore coplex scenarios can be copared As siplest possible case, realizations of processes of iid rando vectors are siulated These siulation results can work as a benchark for ore coplex siulation scenarios The rando vectors under consideration are iid ultivariate noral and ultivariate t distributed with ν = 8 degrees of freedo As covariance atrix the atrices Σ 2 = 07 1, Σ 5 = and Σ 10 = are used as well as identity atrices I p of corresponding diension p To enable a reasonable coparison of the results, the covariance atrices in the case of the t distribution are standardized by ultiplying ν 2 The results are given in Tables 4 and 5 in Appendix B and illustrated ν in Figure 1 For the sake of clarity and since the results differ only slightly for the different values of the tuning paraeter γ and the different types of covariance atrix, the figure only shows the epirical sizes for γ = 0 and an identity covariance atrix The fact that there is hardly a difference in the epirical sizes depending on whether the covariance atrix is diagonal or not was expected as our procedure is only based on estiates of the ain diagonal eleents of the covariance atrix and not of the reaining entries In general, the epirical size increases with the diension In order to deterine the source of this, we use the actual atrix D p that can be easily calculated for an identity covariance atrix I p and its standardized analogue ν 2I ν p, respectively The atrix is given as D p = 2I p for noral distributed rando vectors and as D p = 2(ν 1) I ν 4 p for t distributed ones The results are also given in Tables 4 and 5 in Appendix B and illustrated in Figure 1 They state that the ain fraction of 4
5 Noral distribution Standardized t distribution Epirical size For both graphics: iid: D known iid: D estiated scalar BEKK Epirical size Figure 1: Size coparison: iid rando vectors with atrix D p known and estiated, respectively, and scalar BEKK tie series the increased size is caused by an insufficient estiation of the atrix D p Furtherore, heavy tails in the distribution of the rando vectors entail an additional size increase Unfortunately, the estiation of the atrix D p could not be iproved by using an alternative bandwidth or estiation procedure The epirical size is distinctly larger in the case of the t distributed rando vectors and decreases with growing length of the historical period This convergence to the theoretical size goes back to the fact that all of the asyptotic stateents are established for While for the different values of B - indicating different lengths of the onitoring period - no tendency in the epirical sizes can be recognized, larger values of γ result in a slight increase of the sizes This is a plausible result as larger values of this paraeter tend to sensitize the procedure for changes that are expected early in the onitoring period at the expense of increased probabilities of false alars In the following, the power of the onitoring procedure is investigated considering two different types of scenario In both cases the covariance atrix in the pre-break period equates the atrix Σ p whose diagonal eleents are affected by a structural break later in the series In the first setting, the variances of all coponents increase fro 1 to 13 In the second one, the variance of only one of the coponents jups to 15 In both scenarios the power to detect 5
6 an early and a later occurring change are copared Since the length of the onitoring period depends on the paraeters and B, we assue that, independent of the length of the tie series, the change happens at the sae fraction of the onitoring period indicated by λ (0, 1) We choose λ {005, 05} to ark changepoints located at the beginning (k = 005B) or in the iddle (k = 05B) of the onitoring period The results for the first scenario are given in Tables 6 and 7 in Appendix B and illustrated in Figure 2, while those for the second scenario are presented in Tables 8 and 9 and illustrated in Figure 3 They state that the power increases considerably with growing length of the historical and the onitoring period If all of the variances are affected by a change, the power increases with growing diension of the rando vectors If only one of the variances experiences a change, the frequency of detecting the change decreases for growing diension p since the portion of variance coponents that are not struck by the change increases Early changes can be detected reliably in both scenarios However, the power gets quite low if the changepoint is located in the advanced series, especially for t distributed rando vectors as the rejection fractions in Tables 7 and 9 state The direct coparison of the two scenarios shows that a ajor change in just one of the variances can be detected ore frequently than a inor change that affects all of the variances only when Early change, noral distribution Late change, noral distribution Late change, standardized t distribution Power Power Early change, standardized t distribution Power Power For all graphics: B=05 B=1 B=2 sudden change contin change Figure 2: Power: iid rando vectors when all of the variances are affected by a change 6
7 the diension is rather sall and the change occurs not too late in the onitoring period In all of the settings the procedure perfors worse in the case of t distributed rando vectors, but the differences to the noral distribution results are declining with Also, in ost cases the power is lower for the higher value of γ While for a later change this is a plausible result, it contradicts the expectation that early changes can be detected ore frequently using a higher value of γ An explanation for this result is that in both cases the values of the detector are copared to the values of the scaled threshold function that has a higher slope in the case of the larger tuning paraeter Since both functions intersect the down scaling of the differences by ultiplying k can cause an earlier crossing of the threshold function for γ = 0 than for γ = 025 Overall, changes that occur right after the beginning of the onitoring period can be detected uch ore frequently than those located in the advanced onitoring period no atter how the tuning paraeter was chosen Now, the results can be copared to scenarios of continuously appearing changes, ie, a slow linear increase of the affected variances that starts at λ 1 = 005 and 05, respectively, and is copleted at λ 2 = 03 and 075, respectively The results are also illustrated in Figures 2 and 3 and presented in Tables 6-9 in Appendix B as values in parentheses The ipact of variations Early change, noral distribution Late change, noral distribution Late change, standardized t distribution Power Power Early change, standardized t distribution Power Power For all graphics: B=05 B=1 B=2 sudden change contin change Figure 3: Power: iid rando vectors when only one of the variances is affected by a change 7
8 in the paraeters reains the sae as in the situation of a sudden variance change However, the power is considerably lower in the case of a slow increase Since the power siulations for sudden changes suggest that later changes can be detected less frequently it is clear that changes that are copleted later in the onitoring period are ore difficult to be detected Although in our siulations the detectability of changes that start in the advanced onitoring period is kind of low especially for short historical periods, the power increases quickly with growing length of the historical period 8
9 C Appendix: Tables D is known Σ = Ip Σ = Hp p = 2 γ B = = = Table 4: Size when onitoring a sequence of realizations of iid N ( 0, Σ p ) distributed rando vectors D is known Σ = Ip Σ = Hp p = 2 γ B = = = Table 5: Size when onitoring a sequence of realizations of iid t ν ( 0, ν 2 ν Σ p) distributed rando vectors with ν=8 degrees of freedo 9
10 p = 2 k = 005 k = 05 γ B = = (06665) (08941) (09938) 03398(02276) (03389) (05243) (07960) (09742) (09998) (02798) (04258) (06819) (08972) (09929) (10000) (03336) (05253) (08163) (06482) (08818) (09929) (02073) (03123) (04987) (07848) (09644) (09997) (02599) (03750) (06337) (08689) (09901) (10000) (02890) (04771) (07841) (08929) (09911) (10000) (03564) (05098) (07866) (09671) (09997) (10000) (04431) (06687) (09264) (09934) (10000) (10000) (05245) (07791) 09994(09782) (08852) (09900) 1000 (09999) (03344) (04934) (07501) (09630) (09997) (10000) (04137) (06294) (09044) (09918) (10000) (10000) (04893) (07509) (09725) (09977) (10000) (10000) (06361) (08518) (09870) (10000) (10000) (10000) (07749) (09529) (09994) (10000) (10000) (10000) (08546) (09885) (10000) (09969) (10000) (10000) (06084) (08174) 1000 (09840) (10000) (10000) (10000) (07433) (09434) (09994) (10000) (10000) (10000) (08499) (09868) (10000) Table 6: Power when onitoring a sequence of realizations of iid N ( 0, Σ p ) distributed rando vectors when all of the variances are affected by a change p = 2 k = 005 k = 05 γ B = = (05079) (07059) (09083) (02222) (02635) (03786) (06359) (08363) (09746) (02595) (03329) (04742) (07291) (09032) (09933) (02834) 05 (03715) (05726) (05066) (06833) (08912) (02216) (02454) (03401) (06217) (08100) (09670) (02564) (02967) (04337) (07045) (08896) (09916) (02677) (03450) (05302) (07084) (08636) (09836) (03303) (03801) (05106) (08297) (09547) (09981) (03931) (04719) (06661) (08975) (09827) (09996) (04377) (05446) (07727) (07119) (08603) (09803) (03355) (03700) (04799) (08250) (09503) (09977) (03898) (04536) (06338) (08881) (09807) (09995) (04201) (05294) (07483) (08790) (09687) (09990) (04834) (05246) (06824) (09506) (09939) (1000) (05559) (06592) (08228) (09806) (09990) (10000) (06117) (07545) (09103) (08776) (09651) (09988) (04798) (04983) (06645) (09510) (09919) (10000) (05564) (06292) (08033) (09771) (09986) (10000) (06135) (07175) (08983) Table 7: Power when onitoring a sequence of realizations of iid t ν ( 0, ν 2 ν Σ p) distributed rando vectors with ν=8 degrees of freedo when all of the variances are affected by a change 10
11 p = 2 k = 005 k = 05 γ B = = (09298) (09975) (10000) (04040) (06364) (08923) (09843) (10000) (10000) (05150) (07892) (09784) (09982) (10000) (10000) (06383) (08994) (09970) (09196) (09967) (10000) (03673) (05966) (08792) (09809) (10000) (10000) (04821) (07731) (09712) (09968) (10000) (10000) (05847) (08746) (09953) (08578) (09877) (09996) (03255) (04878) (07774) (09588) (09997) (10000) (04153) (06611) (09283) (09908) (10000) (10000) (07) (07900) (09792) (08443) (09853) (09996) (02945) (04595) (07568) (09533) 10000(09996) (10000) (03952) (06152) (09140) (09890) (10000) (10000) (04722) (07582) (09720) (07481) (09524) (09996) (02557) (03674) (06334) (08996) (09941) (10000) (03417) (05013) (08131) (09530) (09996) (10000) (04093) (06395) (09210) (07444) (09504) (09996) (02543) (03550) (05955) (08892) (09934) (10000) (03244) (04769) (07898) (09477) (09995) (10000) (03821) (06110) (09082) Table 8: Power when onitoring a sequence of realizations of iid N ( 0, Σ p ) distributed rando vectors when only one of the variances is affected by a change p = 2 k = 005 k = 05 γ B = = (07992) (09606) (09989) (03303) (04828) (07289) (09155) (09921) (09997) (04133) (06079) (08709) (09641) (09976) (09999) (04957) (07339) (09512) (07878) (09544) (09986) (03206) (04538) (06931) (09064) (09904) (09997) (03974) (05769) (08427) (09551) (09972) (09998) (04624) (07018) (09395) (07345) (09238) (09968) (03161) (03971) (06091) (08623) (09846) (09997) (03706) (05402) (07864) (09352) (09958) (09998) (04340) (06618) (08855) (07370) (09165) (09961) (03272) (03805) (05871) (08552) (09801) (09997) (03687) (05018) (07646) (09267) (09950) (09998) (04242) (06273) (08746) (06610) (08528) (09843) (03184) (03394) (04896) (08071) (09522) (09989) (03773) (04323) (06423) (08809) (09849) (09994) (04238) (05393) (07700) (06705) (08456) (09806) (03410) (03398) (04607) (08014) (09512) (09983) (03883) (04341) (06176) (08787) (09822) (09993) (04325) (05250) (07451) Table 9: Power when onitoring a sequence of realizations of iid t ν ( 0, ν 2 ν Σ p) distributed rando vectors with ν=8 degrees of freedo when only one of the variances is affected by a change 11
12 ultivariate procedure univariate procedures p = 2 γ B = = = Table 10: Size when onitoring scalar BEKK tie series with paraeters α = 003, β = 045 and N ( 0, Σ p ) distributed innovations ultivariate procedure univariate procedures p = 2 γ B = = = Table 11: Size when onitoring scalar BEKK tie series with paraeters α = 003, β = 045 and t ν ( 0, ν 2 ν Σ p) distributed innovations with ν=8 degrees of freedo p = 2 k = 005 k = 05 γ B = = (06546) (08732) (09900) (02451) (03405) (05131) (07820) (09599) (09990) (02876) (04159) (06522) (08707) (09879) (10000) (03413) (05197) (07794) (06408) (08602) (09869) (02340) (03120) (04760) (07608) (09517) (09988) (02639) (03816) (06150) (08518) (09847) (10000) (03109) (04796) (07428) (08757) (09891) (09999) (03782) (05140) (07645) (09630) (09992) (10000) (04592) (06433) (09010) (09878) (10000) (10000) (05333) (07625) (09622) (08654) (09869) (09999) (03544) (04795) (07298) (09586) (09991) (10000) (04360) (06146) (08840) (09852) (10000) (10000) (08) (07305) (09536) (09964) (10000) (10000) (06333) (08231) (09795) (09999) (10000) (10000) (07639) (09412) (09990) (10000) (10000) (10000) (08492) (09802) (10000) (09957) (10000) (10000) (06086) (08032) (09743) (09999) (10000) (10000) (07415) (09288) (09983) (10000) (10000) (10000) (08321) (09765) (10000) Table 12: Power when onitoring scalar BEKK tie series and all of the variances increase (N ( ) 0, Σ p distributed innovations) 12
13 p = 2 k = 005 k = 05 γ B = = (05036) (06778) (08787) (02225) (02525) (03506) (06175) (08044) (09580) (02602) (03140) (04451) (07052) (08835) (09881) (02922) (03749) (05585) (05168) (06812) (08763) (02418) (02598) (03347) (06213) (07956) (09558) (02743) (03116) (04272) (06948) (08755) (09847) (02835) (03575) (05266) (07018) (08550) (09762) (03476) (03916) (05033) (08171) (09466) (09971) (04188) (04707) (06412) (08823) (09774) (09997) (04534) (05464) (07491) (07103) (08517) (09716) (03645) (03797) (04745) (08188) (09348) (09953) (04077) (04593) (06193) (08838) (09751) (09992) (04555) (05378) (07240) (08772) (09609) (09988) (05284) (05673) (06859) (09403) (09928) (09998) (05768) (06494) (08109) (09798) (09979) (10000) (06480) (07476) (09011) (08755) (09549) (09977) (05190) (05357) (06618) (09463) (09932) (10000) (05770) (06474) (07978) (09730) (09981) (10000) (06399) (07114) (08835) Table ( 13: Power when onitoring scalar BEKK tie series and all of the variances increase (t ν 0, ν 2 ν Σ p) distributed innovations with ν=8 degrees of freedo) p = 2 k = 005 k = 05 γ B = = (09063) (09950) (10000) (03937) (06026) (08623) (09794) (09995) (10000) (05065) (07684) (09646) (09954) (10000) (10000) (06141) (08814) (09938) (08979) (09926) (10000) (03747) (05614) (08442) (09721) (09996) (10000) (04712) (07320) (09583) (09948) (10000) (10000) (05855) (08482) (09906) (08341) (09784) (10000) (03264) (04779) (07516) (09454) (09985) (10000) (04172) (06438) (09058) (09862) (10000) (10000) (05058) (07637) (09696) (08256) (09760) (09999) (03021) (04463) (07299) (09364) (09985) (10000) (03930) (06079) (08873) (09811) (10000) (10000) (04869) (07326) (09614) (07390) (09396) (09985) (02859) (03695) (06011) (08844) (09919) (10000) (03666) (05067) (07968) (09499) (09995) (10000) (04210) (06228) (08966) (07231) (09302) (09980) (02779) (03554) (05619) (08729) (09882) (10000) (03485) (04888) (07668) (09483) (09982) (10000) (03947) (05893) (08758) Table 14: Power when onitoring scalar BEKK tie series and just one of the variances increases (N ( 0, Σ p ) distributed innovations) 13
14 p = 2 k = 005 k = 05 γ B = = (07823) (09444) (09982) (03340) (04609) (07014) (09004) (09895) (09997) (04263) (06036) (08481) (09540) (09972) (10000) (04919) (07163) (09296) (07725) (09365) (09977) (03186) (04463) (06724) (08842) (09870) (09996) (04001) (05738) (08206) (09450) (09970) (09998) (04827) (06907) (09206) (07142) (09085) (09929) (03175) (03925) (05881) (08439) (09759) (09997) (03904) (05086) (07587) (09233) (09946) (10000) (04487) (06239) (08684) (07168) (08983) (09940) (03304) (03863) (05621) (08507) (09773) (09994) (04003) (05138) (07378) (09207) (09925) (09999) (04460) (05954) (08456) (06705) (08354) (09750) (03587) (03673) (04872) (07969) (09419) (09984) (03983) (04642) (06375) (08736) (09747) (09993) (04425) (05159) (07415) (06736) (08235) (09700) (03761) (03648) (04611) (07939) (09367) (09960) (04322) (04526) (06152) (08691) (09741) (09993) (04655) (05185) (07241) Table 15: Power when onitoring scalar BEKK tie series and just one of the variances increases (t ν ( 0, ν 2 ν Σ p) distributed innovations with ν=8 degrees of freedo) p = 2 noral distribution t distribution k = 005 k = 05 k = 005 k = 05 γ B = = = = Table 16: Power when using univariate onitoring procedures: scalar BEKK tie series and all of the variances increase 14
15 p = 2 noral distribution t distribution k = 005 k = 05 k = 005 k = 05 γ B = = = = Table 17: Power when using univariate onitoring procedures: scalar BEKK tie series and only one of the variances increases p = 2 noral distribution t distribution k = 005 k = 05 k = 005 k = 05 γ B = = = = Table 18: Power when the variance of the innovations increases 15
16 References Davidson, J (1994): Stochastic Liit Theory, Oxford University Press Engle, R and K Kroner (1995): Multivariate Siultaneaous Generalized Arch, Econoetric Theory, 11, Hafner, C (2003): Fourth Moent Structure of Multivariate GARCH Models, Journal of Financial Econoetrics, 1(1), Wied, D, M Arnold, N Bissantz, and D Ziggel (2012a): A New Fluctuation Test for Constant Variances with Applications to Finance, Metrika, 75(8), Wied, D and P Galeano (2013): Monitoring Correlation Change in a Sequence of Rando Variables, Journal of Statistical Planning and Inference, 143(1), Wied, D, W Kräer, and H Dehling (2012b): Testing for a Change in Correlation at an Unknown Point in Tie Using an Extended Functional Delta Method, Econoetric Theory, 68(3),
Keywords: Estimator, Bias, Mean-squared error, normality, generalized Pareto distribution
Testing approxiate norality of an estiator using the estiated MSE and bias with an application to the shape paraeter of the generalized Pareto distribution J. Martin van Zyl Abstract In this work the norality
More informationarxiv: v1 [stat.ot] 7 Jul 2010
Hotelling s test for highly correlated data P. Bubeliny e-ail: bubeliny@karlin.ff.cuni.cz Charles University, Faculty of Matheatics and Physics, KPMS, Sokolovska 83, Prague, Czech Republic, 8675. arxiv:007.094v
More informationSome Proofs: This section provides proofs of some theoretical results in section 3.
Testing Jups via False Discovery Rate Control Yu-Min Yen. Institute of Econoics, Acadeia Sinica, Taipei, Taiwan. E-ail: YMYEN@econ.sinica.edu.tw. SUPPLEMENTARY MATERIALS Suppleentary Materials contain
More informationBlock designs and statistics
Bloc designs and statistics Notes for Math 447 May 3, 2011 The ain paraeters of a bloc design are nuber of varieties v, bloc size, nuber of blocs b. A design is built on a set of v eleents. Each eleent
More informationExtension of CSRSM for the Parametric Study of the Face Stability of Pressurized Tunnels
Extension of CSRSM for the Paraetric Study of the Face Stability of Pressurized Tunnels Guilhe Mollon 1, Daniel Dias 2, and Abdul-Haid Soubra 3, M.ASCE 1 LGCIE, INSA Lyon, Université de Lyon, Doaine scientifique
More informationTesting equality of variances for multiple univariate normal populations
University of Wollongong Research Online Centre for Statistical & Survey Methodology Working Paper Series Faculty of Engineering and Inforation Sciences 0 esting equality of variances for ultiple univariate
More information13.2 Fully Polynomial Randomized Approximation Scheme for Permanent of Random 0-1 Matrices
CS71 Randoness & Coputation Spring 018 Instructor: Alistair Sinclair Lecture 13: February 7 Disclaier: These notes have not been subjected to the usual scrutiny accorded to foral publications. They ay
More informationMulti-Dimensional Hegselmann-Krause Dynamics
Multi-Diensional Hegselann-Krause Dynaics A. Nedić Industrial and Enterprise Systes Engineering Dept. University of Illinois Urbana, IL 680 angelia@illinois.edu B. Touri Coordinated Science Laboratory
More informationChapter 6 1-D Continuous Groups
Chapter 6 1-D Continuous Groups Continuous groups consist of group eleents labelled by one or ore continuous variables, say a 1, a 2,, a r, where each variable has a well- defined range. This chapter explores:
More informationA Jackknife Correction to a Test for Cointegration Rank
Econoetrics 205, 3, 355-375; doi:0.3390/econoetrics3020355 OPEN ACCESS econoetrics ISSN 2225-46 www.dpi.co/journal/econoetrics Article A Jackknife Correction to a Test for Cointegration Rank Marcus J.
More informationA remark on a success rate model for DPA and CPA
A reark on a success rate odel for DPA and CPA A. Wieers, BSI Version 0.5 andreas.wieers@bsi.bund.de Septeber 5, 2018 Abstract The success rate is the ost coon evaluation etric for easuring the perforance
More informationTesting the lag length of vector autoregressive models: A power comparison between portmanteau and Lagrange multiplier tests
Working Papers 2017-03 Testing the lag length of vector autoregressive odels: A power coparison between portanteau and Lagrange ultiplier tests Raja Ben Hajria National Engineering School, University of
More informationSharp Time Data Tradeoffs for Linear Inverse Problems
Sharp Tie Data Tradeoffs for Linear Inverse Probles Saet Oyak Benjain Recht Mahdi Soltanolkotabi January 016 Abstract In this paper we characterize sharp tie-data tradeoffs for optiization probles used
More informationNon-Parametric Non-Line-of-Sight Identification 1
Non-Paraetric Non-Line-of-Sight Identification Sinan Gezici, Hisashi Kobayashi and H. Vincent Poor Departent of Electrical Engineering School of Engineering and Applied Science Princeton University, Princeton,
More informationA note on the multiplication of sparse matrices
Cent. Eur. J. Cop. Sci. 41) 2014 1-11 DOI: 10.2478/s13537-014-0201-x Central European Journal of Coputer Science A note on the ultiplication of sparse atrices Research Article Keivan Borna 12, Sohrab Aboozarkhani
More information3.3 Variational Characterization of Singular Values
3.3. Variational Characterization of Singular Values 61 3.3 Variational Characterization of Singular Values Since the singular values are square roots of the eigenvalues of the Heritian atrices A A and
More informationarxiv: v2 [math.st] 11 Dec 2018
esting for high-diensional network paraeters in auto-regressive odels arxiv:803659v [aths] Dec 08 Lili Zheng and Garvesh Raskutti Abstract High-diensional auto-regressive odels provide a natural way to
More informationSupport recovery in compressed sensing: An estimation theoretic approach
Support recovery in copressed sensing: An estiation theoretic approach Ain Karbasi, Ali Horati, Soheil Mohajer, Martin Vetterli School of Coputer and Counication Sciences École Polytechnique Fédérale de
More informationare equal to zero, where, q = p 1. For each gene j, the pairwise null and alternative hypotheses are,
Page of 8 Suppleentary Materials: A ultiple testing procedure for ulti-diensional pairwise coparisons with application to gene expression studies Anjana Grandhi, Wenge Guo, Shyaal D. Peddada S Notations
More informationThe Distribution of the Covariance Matrix for a Subset of Elliptical Distributions with Extension to Two Kurtosis Parameters
journal of ultivariate analysis 58, 96106 (1996) article no. 0041 The Distribution of the Covariance Matrix for a Subset of Elliptical Distributions with Extension to Two Kurtosis Paraeters H. S. Steyn
More informationRandom Process Review
Rando Process Review Consider a rando process t, and take k saples. For siplicity, we will set k. However it should ean any nuber of saples. t () t x t, t, t We have a rando vector t, t, t. If we find
More informationCS Lecture 13. More Maximum Likelihood
CS 6347 Lecture 13 More Maxiu Likelihood Recap Last tie: Introduction to axiu likelihood estiation MLE for Bayesian networks Optial CPTs correspond to epirical counts Today: MLE for CRFs 2 Maxiu Likelihood
More informationPhysics 215 Winter The Density Matrix
Physics 215 Winter 2018 The Density Matrix The quantu space of states is a Hilbert space H. Any state vector ψ H is a pure state. Since any linear cobination of eleents of H are also an eleent of H, it
More informationKernel-Based Nonparametric Anomaly Detection
Kernel-Based Nonparaetric Anoaly Detection Shaofeng Zou Dept of EECS Syracuse University Eail: szou@syr.edu Yingbin Liang Dept of EECS Syracuse University Eail: yliang6@syr.edu H. Vincent Poor Dept of
More informationCOS 424: Interacting with Data. Written Exercises
COS 424: Interacting with Data Hoework #4 Spring 2007 Regression Due: Wednesday, April 18 Written Exercises See the course website for iportant inforation about collaboration and late policies, as well
More informationConvergence of a Moran model to Eigen s quasispecies model
Convergence of a Moran odel to Eigen s quasispecies odel Joseba Dalau Université Paris Sud and ENS Paris June 6, 2018 arxiv:1404.2133v1 [q-bio.pe] 8 Apr 2014 Abstract We prove that a Moran odel converges
More informationUsing a De-Convolution Window for Operating Modal Analysis
Using a De-Convolution Window for Operating Modal Analysis Brian Schwarz Vibrant Technology, Inc. Scotts Valley, CA Mark Richardson Vibrant Technology, Inc. Scotts Valley, CA Abstract Operating Modal Analysis
More informationSupplementary Information for Design of Bending Multi-Layer Electroactive Polymer Actuators
Suppleentary Inforation for Design of Bending Multi-Layer Electroactive Polyer Actuators Bavani Balakrisnan, Alek Nacev, and Elisabeth Sela University of Maryland, College Park, Maryland 074 1 Analytical
More informationCourse Notes for EE227C (Spring 2018): Convex Optimization and Approximation
Course Notes for EE7C (Spring 018: Convex Optiization and Approxiation Instructor: Moritz Hardt Eail: hardt+ee7c@berkeley.edu Graduate Instructor: Max Sichowitz Eail: sichow+ee7c@berkeley.edu October 15,
More informationESTIMATING AND FORMING CONFIDENCE INTERVALS FOR EXTREMA OF RANDOM POLYNOMIALS. A Thesis. Presented to. The Faculty of the Department of Mathematics
ESTIMATING AND FORMING CONFIDENCE INTERVALS FOR EXTREMA OF RANDOM POLYNOMIALS A Thesis Presented to The Faculty of the Departent of Matheatics San Jose State University In Partial Fulfillent of the Requireents
More informationThe Hilbert Schmidt version of the commutator theorem for zero trace matrices
The Hilbert Schidt version of the coutator theore for zero trace atrices Oer Angel Gideon Schechtan March 205 Abstract Let A be a coplex atrix with zero trace. Then there are atrices B and C such that
More informationGEE ESTIMATORS IN MIXTURE MODEL WITH VARYING CONCENTRATIONS
ACTA UIVERSITATIS LODZIESIS FOLIA OECOOMICA 3(3142015 http://dx.doi.org/10.18778/0208-6018.314.03 Olesii Doronin *, Rostislav Maiboroda ** GEE ESTIMATORS I MIXTURE MODEL WITH VARYIG COCETRATIOS Abstract.
More informationFeature Extraction Techniques
Feature Extraction Techniques Unsupervised Learning II Feature Extraction Unsupervised ethods can also be used to find features which can be useful for categorization. There are unsupervised ethods that
More informationPoornima University, For any query, contact us at: , 18
AIEEE//Math S. No Questions Solutions Q. Lets cos (α + β) = and let sin (α + β) = 5, where α, β π, then tan α = 5 (a) 56 (b) 9 (c) 7 (d) 5 6 Sol: (a) cos (α + β) = 5 tan (α + β) = tan α = than (α + β +
More informationOn the block maxima method in extreme value theory
On the bloc axiethod in extree value theory Ana Ferreira ISA, Univ Tecn Lisboa, Tapada da Ajuda 349-7 Lisboa, Portugal CEAUL, FCUL, Bloco C6 - Piso 4 Capo Grande, 749-6 Lisboa, Portugal anafh@isa.utl.pt
More informationResearch Article On the Isolated Vertices and Connectivity in Random Intersection Graphs
International Cobinatorics Volue 2011, Article ID 872703, 9 pages doi:10.1155/2011/872703 Research Article On the Isolated Vertices and Connectivity in Rando Intersection Graphs Yilun Shang Institute for
More informationTEST OF HOMOGENEITY OF PARALLEL SAMPLES FROM LOGNORMAL POPULATIONS WITH UNEQUAL VARIANCES
TEST OF HOMOGENEITY OF PARALLEL SAMPLES FROM LOGNORMAL POPULATIONS WITH UNEQUAL VARIANCES S. E. Ahed, R. J. Tokins and A. I. Volodin Departent of Matheatics and Statistics University of Regina Regina,
More informationInteractive Markov Models of Evolutionary Algorithms
Cleveland State University EngagedScholarship@CSU Electrical Engineering & Coputer Science Faculty Publications Electrical Engineering & Coputer Science Departent 2015 Interactive Markov Models of Evolutionary
More informationData-Driven Imaging in Anisotropic Media
18 th World Conference on Non destructive Testing, 16- April 1, Durban, South Africa Data-Driven Iaging in Anisotropic Media Arno VOLKER 1 and Alan HUNTER 1 TNO Stieltjesweg 1, 6 AD, Delft, The Netherlands
More informationLocal asymptotic powers of nonparametric and semiparametric tests for fractional integration
Stochastic Processes and their Applications 117 (2007) 251 261 www.elsevier.co/locate/spa Local asyptotic powers of nonparaetric and seiparaetric tests for fractional integration Xiaofeng Shao, Wei Biao
More informationCh 12: Variations on Backpropagation
Ch 2: Variations on Backpropagation The basic backpropagation algorith is too slow for ost practical applications. It ay take days or weeks of coputer tie. We deonstrate why the backpropagation algorith
More informationE0 370 Statistical Learning Theory Lecture 6 (Aug 30, 2011) Margin Analysis
E0 370 tatistical Learning Theory Lecture 6 (Aug 30, 20) Margin Analysis Lecturer: hivani Agarwal cribe: Narasihan R Introduction In the last few lectures we have seen how to obtain high confidence bounds
More informationIn this chapter, we consider several graph-theoretic and probabilistic models
THREE ONE GRAPH-THEORETIC AND STATISTICAL MODELS 3.1 INTRODUCTION In this chapter, we consider several graph-theoretic and probabilistic odels for a social network, which we do under different assuptions
More informationOptimal Jamming Over Additive Noise: Vector Source-Channel Case
Fifty-first Annual Allerton Conference Allerton House, UIUC, Illinois, USA October 2-3, 2013 Optial Jaing Over Additive Noise: Vector Source-Channel Case Erah Akyol and Kenneth Rose Abstract This paper
More informationCSE525: Randomized Algorithms and Probabilistic Analysis May 16, Lecture 13
CSE55: Randoied Algoriths and obabilistic Analysis May 6, Lecture Lecturer: Anna Karlin Scribe: Noah Siegel, Jonathan Shi Rando walks and Markov chains This lecture discusses Markov chains, which capture
More informationOBJECTIVES INTRODUCTION
M7 Chapter 3 Section 1 OBJECTIVES Suarize data using easures of central tendency, such as the ean, edian, ode, and idrange. Describe data using the easures of variation, such as the range, variance, and
More informationW-BASED VS LATENT VARIABLES SPATIAL AUTOREGRESSIVE MODELS: EVIDENCE FROM MONTE CARLO SIMULATIONS
W-BASED VS LATENT VARIABLES SPATIAL AUTOREGRESSIVE MODELS: EVIDENCE FROM MONTE CARLO SIMULATIONS. Introduction When it coes to applying econoetric odels to analyze georeferenced data, researchers are well
More informationKinetic Theory of Gases: Elementary Ideas
Kinetic Theory of Gases: Eleentary Ideas 17th February 2010 1 Kinetic Theory: A Discussion Based on a Siplified iew of the Motion of Gases 1.1 Pressure: Consul Engel and Reid Ch. 33.1) for a discussion
More informationBootstrapping Dependent Data
Bootstrapping Dependent Data One of the key issues confronting bootstrap resapling approxiations is how to deal with dependent data. Consider a sequence fx t g n t= of dependent rando variables. Clearly
More informationDEPARTMENT OF ECONOMETRICS AND BUSINESS STATISTICS
ISSN 1440-771X AUSTRALIA DEPARTMENT OF ECONOMETRICS AND BUSINESS STATISTICS An Iproved Method for Bandwidth Selection When Estiating ROC Curves Peter G Hall and Rob J Hyndan Working Paper 11/00 An iproved
More informationImage Reconstruction by means of Kalman Filtering in Passive Millimetre- Wave Imaging
Iage Reconstruction by eans of Kalan Filtering in assive illietre- Wave Iaging David Sith, etrie eyer, Ben Herbst 2 Departent of Electrical and Electronic Engineering, University of Stellenbosch, rivate
More informationWarning System of Dangerous Chemical Gas in Factory Based on Wireless Sensor Network
565 A publication of CHEMICAL ENGINEERING TRANSACTIONS VOL. 59, 07 Guest Editors: Zhuo Yang, Junie Ba, Jing Pan Copyright 07, AIDIC Servizi S.r.l. ISBN 978-88-95608-49-5; ISSN 83-96 The Italian Association
More informationPORTMANTEAU TESTS FOR ARMA MODELS WITH INFINITE VARIANCE
doi:10.1111/j.1467-9892.2007.00572.x PORTMANTEAU TESTS FOR ARMA MODELS WITH INFINITE VARIANCE By J.-W. Lin and A. I. McLeod The University of Western Ontario First Version received Septeber 2006 Abstract.
More informationThis model assumes that the probability of a gap has size i is proportional to 1/i. i.e., i log m e. j=1. E[gap size] = i P r(i) = N f t.
CS 493: Algoriths for Massive Data Sets Feb 2, 2002 Local Models, Bloo Filter Scribe: Qin Lv Local Models In global odels, every inverted file entry is copressed with the sae odel. This work wells when
More informationThe degree of a typical vertex in generalized random intersection graph models
Discrete Matheatics 306 006 15 165 www.elsevier.co/locate/disc The degree of a typical vertex in generalized rando intersection graph odels Jerzy Jaworski a, Michał Karoński a, Dudley Stark b a Departent
More informationSupplementary Materials: Proofs and Technical Details for Parsimonious Tensor Response Regression Lexin Li and Xin Zhang
Suppleentary Materials: Proofs and Tecnical Details for Parsionious Tensor Response Regression Lexin Li and Xin Zang A Soe preliinary results We will apply te following two results repeatedly. For a positive
More informationBest Linear Unbiased and Invariant Reconstructors for the Past Records
BULLETIN of the MALAYSIAN MATHEMATICAL SCIENCES SOCIETY http:/athusy/bulletin Bull Malays Math Sci Soc (2) 37(4) (2014), 1017 1028 Best Linear Unbiased and Invariant Reconstructors for the Past Records
More informationIntelligent Systems: Reasoning and Recognition. Artificial Neural Networks
Intelligent Systes: Reasoning and Recognition Jaes L. Crowley MOSIG M1 Winter Seester 2018 Lesson 7 1 March 2018 Outline Artificial Neural Networks Notation...2 Introduction...3 Key Equations... 3 Artificial
More informationPattern Recognition and Machine Learning. Artificial Neural networks
Pattern Recognition and Machine Learning Jaes L. Crowley ENSIMAG 3 - MMIS Fall Seester 2017 Lessons 7 20 Dec 2017 Outline Artificial Neural networks Notation...2 Introduction...3 Key Equations... 3 Artificial
More informationLecture 9 November 23, 2015
CSC244: Discrepancy Theory in Coputer Science Fall 25 Aleksandar Nikolov Lecture 9 Noveber 23, 25 Scribe: Nick Spooner Properties of γ 2 Recall that γ 2 (A) is defined for A R n as follows: γ 2 (A) = in{r(u)
More informationKinetic Theory of Gases: Elementary Ideas
Kinetic Theory of Gases: Eleentary Ideas 9th February 011 1 Kinetic Theory: A Discussion Based on a Siplified iew of the Motion of Gases 1.1 Pressure: Consul Engel and Reid Ch. 33.1) for a discussion of
More informationLean Walsh Transform
Lean Walsh Transfor Edo Liberty 5th March 007 inforal intro We show an orthogonal atrix A of size d log 4 3 d (α = log 4 3) which is applicable in tie O(d). By applying a rando sign change atrix S to the
More informationOptical Properties of Plasmas of High-Z Elements
Forschungszentru Karlsruhe Techni und Uwelt Wissenschaftlishe Berichte FZK Optical Properties of Plasas of High-Z Eleents V.Tolach 1, G.Miloshevsy 1, H.Würz Project Kernfusion 1 Heat and Mass Transfer
More informationAN OPTIMAL SHRINKAGE FACTOR IN PREDICTION OF ORDERED RANDOM EFFECTS
Statistica Sinica 6 016, 1709-178 doi:http://dx.doi.org/10.5705/ss.0014.0034 AN OPTIMAL SHRINKAGE FACTOR IN PREDICTION OF ORDERED RANDOM EFFECTS Nilabja Guha 1, Anindya Roy, Yaakov Malinovsky and Gauri
More informationRandomized Recovery for Boolean Compressed Sensing
Randoized Recovery for Boolean Copressed Sensing Mitra Fatei and Martin Vetterli Laboratory of Audiovisual Counication École Polytechnique Fédéral de Lausanne (EPFL) Eail: {itra.fatei, artin.vetterli}@epfl.ch
More informationQuantum algorithms (CO 781, Winter 2008) Prof. Andrew Childs, University of Waterloo LECTURE 15: Unstructured search and spatial search
Quantu algoriths (CO 781, Winter 2008) Prof Andrew Childs, University of Waterloo LECTURE 15: Unstructured search and spatial search ow we begin to discuss applications of quantu walks to search algoriths
More informationTail estimates for norms of sums of log-concave random vectors
Tail estiates for nors of sus of log-concave rando vectors Rados law Adaczak Rafa l Lata la Alexander E. Litvak Alain Pajor Nicole Toczak-Jaegerann Abstract We establish new tail estiates for order statistics
More information1 Generalization bounds based on Rademacher complexity
COS 5: Theoretical Machine Learning Lecturer: Rob Schapire Lecture #0 Scribe: Suqi Liu March 07, 08 Last tie we started proving this very general result about how quickly the epirical average converges
More informationA Powerful Portmanteau Test of Lack of Fit for Time Series
A Powerful Portanteau Test of Lack of Fit for Tie Series Daniel Peña and Julio Rodríguez A new portanteau test for tie series, ore powerful than the tests of Ljung and Box and Monti, is proposed. The test
More informationStatistical Logic Cell Delay Analysis Using a Current-based Model
Statistical Logic Cell Delay Analysis Using a Current-based Model Hanif Fatei Shahin Nazarian Massoud Pedra Dept. of EE-Systes, University of Southern California, Los Angeles, CA 90089 {fatei, shahin,
More informationON A SIRV-CFAR DETECTOR WITH RADAR EXPERIMENTATIONS IN IMPULSIVE CLUTTER
O A SIRV-CFAR DETECTOR WITH RADAR EXPERIMETATIOS I IMPULSIVE CLUTTER Frédéric Pascal 23, Jean-Philippe Ovarlez, Philippe Forster 2, and Pascal Larzabal 3 OERA DEMR/TSI Chein de la Hunière, F-976, Palaiseau
More informationA Bernstein-Markov Theorem for Normed Spaces
A Bernstein-Markov Theore for Nored Spaces Lawrence A. Harris Departent of Matheatics, University of Kentucky Lexington, Kentucky 40506-0027 Abstract Let X and Y be real nored linear spaces and let φ :
More informationChaotic Coupled Map Lattices
Chaotic Coupled Map Lattices Author: Dustin Keys Advisors: Dr. Robert Indik, Dr. Kevin Lin 1 Introduction When a syste of chaotic aps is coupled in a way that allows the to share inforation about each
More informationA New Class of APEX-Like PCA Algorithms
Reprinted fro Proceedings of ISCAS-98, IEEE Int. Syposiu on Circuit and Systes, Monterey (USA), June 1998 A New Class of APEX-Like PCA Algoriths Sione Fiori, Aurelio Uncini, Francesco Piazza Dipartiento
More informationFundamental Limits of Database Alignment
Fundaental Liits of Database Alignent Daniel Cullina Dept of Electrical Engineering Princeton University dcullina@princetonedu Prateek Mittal Dept of Electrical Engineering Princeton University pittal@princetonedu
More informationSemicircle law for generalized Curie-Weiss matrix ensembles at subcritical temperature
Seicircle law for generalized Curie-Weiss atrix ensebles at subcritical teperature Werner Kirsch Fakultät für Matheatik und Inforatik FernUniversität in Hagen, Gerany Thoas Kriecherbauer Matheatisches
More informationCharacterization of the Line Complexity of Cellular Automata Generated by Polynomial Transition Rules. Bertrand Stone
Characterization of the Line Coplexity of Cellular Autoata Generated by Polynoial Transition Rules Bertrand Stone Abstract Cellular autoata are discrete dynaical systes which consist of changing patterns
More informationA general forulation of the cross-nested logit odel Michel Bierlaire, Dpt of Matheatics, EPFL, Lausanne Phone: Fax:
A general forulation of the cross-nested logit odel Michel Bierlaire, EPFL Conference paper STRC 2001 Session: Choices A general forulation of the cross-nested logit odel Michel Bierlaire, Dpt of Matheatics,
More informationConsistent Multiclass Algorithms for Complex Performance Measures. Supplementary Material
Consistent Multiclass Algoriths for Coplex Perforance Measures Suppleentary Material Notations. Let λ be the base easure over n given by the unifor rando variable (say U over n. Hence, for all easurable
More informationNonlinear Log-Periodogram Regression for Perturbed Fractional Processes
Nonlinear Log-Periodogra Regression for Perturbed Fractional Processes Yixiao Sun Departent of Econoics Yale University Peter C. B. Phillips Cowles Foundation for Research in Econoics Yale University First
More informationSynchronization in large directed networks of coupled phase oscillators
CHAOS 16, 015107 2005 Synchronization in large directed networks of coupled phase oscillators Juan G. Restrepo a Institute for Research in Electronics and Applied Physics, University of Maryland, College
More informationEE5900 Spring Lecture 4 IC interconnect modeling methods Zhuo Feng
EE59 Spring Parallel LSI AD Algoriths Lecture I interconnect odeling ethods Zhuo Feng. Z. Feng MTU EE59 So far we ve considered only tie doain analyses We ll soon see that it is soeties preferable to odel
More informationarxiv: v2 [math.co] 3 Dec 2008
arxiv:0805.2814v2 [ath.co] 3 Dec 2008 Connectivity of the Unifor Rando Intersection Graph Sion R. Blacburn and Stefanie Gere Departent of Matheatics Royal Holloway, University of London Egha, Surrey TW20
More informationMoments of the product and ratio of two correlated chi-square variables
Stat Papers 009 50:581 59 DOI 10.1007/s0036-007-0105-0 REGULAR ARTICLE Moents of the product and ratio of two correlated chi-square variables Anwar H. Joarder Received: June 006 / Revised: 8 October 007
More informationAnalyzing Simulation Results
Analyzing Siulation Results Dr. John Mellor-Cruey Departent of Coputer Science Rice University johnc@cs.rice.edu COMP 528 Lecture 20 31 March 2005 Topics for Today Model verification Model validation Transient
More informationWhat is the instantaneous acceleration (2nd derivative of time) of the field? Sol. The Euler-Lagrange equations quickly yield:
PHYSICS 75: The Standard Model Midter Exa Solution Key. [3 points] Short Answer (6 points each (a In words, explain how to deterine the nuber of ediator particles are generated by a particular local gauge
More informationInspection; structural health monitoring; reliability; Bayesian analysis; updating; decision analysis; value of information
Cite as: Straub D. (2014). Value of inforation analysis with structural reliability ethods. Structural Safety, 49: 75-86. Value of Inforation Analysis with Structural Reliability Methods Daniel Straub
More informationRAFIA(MBA) TUTOR S UPLOADED FILE Course STA301: Statistics and Probability Lecture No 1 to 5
Course STA0: Statistics and Probability Lecture No to 5 Multiple Choice Questions:. Statistics deals with: a) Observations b) Aggregates of facts*** c) Individuals d) Isolated ites. A nuber of students
More informationFAST DYNAMO ON THE REAL LINE
FAST DYAMO O THE REAL LIE O. KOZLOVSKI & P. VYTOVA Abstract. In this paper we show that a piecewise expanding ap on the interval, extended to the real line by a non-expanding ap satisfying soe ild hypthesis
More information2 Q 10. Likewise, in case of multiple particles, the corresponding density in 2 must be averaged over all
Lecture 6 Introduction to kinetic theory of plasa waves Introduction to kinetic theory So far we have been odeling plasa dynaics using fluid equations. The assuption has been that the pressure can be either
More informationBootstrapping clustered data
J. R. Statist. Soc. B (2007) 69, Part 3, pp. 369 390 Bootstrapping clustered data C. A. Field Dalhousie University, Halifax, Canada A. H. Welsh Australian National University, Canberra, Australia [Received
More informationIntelligent Systems: Reasoning and Recognition. Perceptrons and Support Vector Machines
Intelligent Systes: Reasoning and Recognition Jaes L. Crowley osig 1 Winter Seester 2018 Lesson 6 27 February 2018 Outline Perceptrons and Support Vector achines Notation...2 Linear odels...3 Lines, Planes
More informationUnderstanding Machine Learning Solution Manual
Understanding Machine Learning Solution Manual Written by Alon Gonen Edited by Dana Rubinstein Noveber 17, 2014 2 Gentle Start 1. Given S = ((x i, y i )), define the ultivariate polynoial p S (x) = i []:y
More informationRecursive Algebraic Frisch Scheme: a Particle-Based Approach
Recursive Algebraic Frisch Schee: a Particle-Based Approach Stefano Massaroli Renato Myagusuku Federico Califano Claudio Melchiorri Atsushi Yaashita Hajie Asaa Departent of Precision Engineering, The University
More informationAn Adaptive UKF Algorithm for the State and Parameter Estimations of a Mobile Robot
Vol. 34, No. 1 ACTA AUTOMATICA SINICA January, 2008 An Adaptive UKF Algorith for the State and Paraeter Estiations of a Mobile Robot SONG Qi 1, 2 HAN Jian-Da 1 Abstract For iproving the estiation accuracy
More informationLogLog-Beta and More: A New Algorithm for Cardinality Estimation Based on LogLog Counting
LogLog-Beta and More: A New Algorith for Cardinality Estiation Based on LogLog Counting Jason Qin, Denys Ki, Yuei Tung The AOLP Core Data Service, AOL, 22000 AOL Way Dulles, VA 20163 E-ail: jasonqin@teaaolco
More informationSHORT TIME FOURIER TRANSFORM PROBABILITY DISTRIBUTION FOR TIME-FREQUENCY SEGMENTATION
SHORT TIME FOURIER TRANSFORM PROBABILITY DISTRIBUTION FOR TIME-FREQUENCY SEGMENTATION Fabien Millioz, Julien Huillery, Nadine Martin To cite this version: Fabien Millioz, Julien Huillery, Nadine Martin.
More informationA method to determine relative stroke detection efficiencies from multiplicity distributions
A ethod to deterine relative stroke detection eiciencies ro ultiplicity distributions Schulz W. and Cuins K. 2. Austrian Lightning Detection and Inoration Syste (ALDIS), Kahlenberger Str.2A, 90 Vienna,
More informationA Better Algorithm For an Ancient Scheduling Problem. David R. Karger Steven J. Phillips Eric Torng. Department of Computer Science
A Better Algorith For an Ancient Scheduling Proble David R. Karger Steven J. Phillips Eric Torng Departent of Coputer Science Stanford University Stanford, CA 9435-4 Abstract One of the oldest and siplest
More informationComputational and Statistical Learning Theory
Coputational and Statistical Learning Theory Proble sets 5 and 6 Due: Noveber th Please send your solutions to learning-subissions@ttic.edu Notations/Definitions Recall the definition of saple based Radeacher
More information