Mixtures Experiments with Mixing Errors
|
|
- Lewis Russell
- 6 years ago
- Views:
Transcription
1 Mures Epermens h Mng Errors Aaa Ahuba & Aeander N. Donev Frs verson: June 009 Research Repor No. 0, 009, Probaby and Sascs Group Schoo o Mahemacs, he Unversy o Mancheser
2 Mures Epermens h Mng Errors Aaa Ahuba and Aeander N. Donev Schoo o Mahemacs, Unversy o Mancheser, UK Absrac. Varous properes o mure producs depend on he proporons o he componens o he mure, bu no on s amoun. In a mure epermen he mures are prepared by mng he reured amouns o mure componens. hs paper consders he mpac o mng errors on he sasca anayss o such daa. Keyords: errors n varabes, regresson cabraon, Scheé poynoma, smpe ace desgn.
3 . Inroducon he man properes o many producs produced by mng severa componens depend on her proporons n he mure bu no on he amoun o he mure. ypca eampes are he ase o a bend o ru uces obaned rom deren rus and he srengh o an aoy made by mng deren meas. here are aso cases here oher acors may aso aec he properes o he mure. For eampe, he eec o a drug combnaon or a erzer made o severa ngredens oud depend no ony on he proporons o componens o he mure bu aso on s amoun and he ay s manuacured and apped. Mures h reured proporons o he ngredens are usuay obaned by mng approprae amouns o hem. hs s oen done h errors hch haever sma can nuence he properes o he mure. e nvesgae he mpac o such errors on he sasca anayss o daa coeced n epermens h mures and sugges mprovemens o he anayss ha gnores he mng errors. e sho ha hese resus aso ao or evauang and conrong he cos o manuacurng mure producs h mng errors. he probem o errors n varabes has receved consderabe aenon n he eraure. Monographs summarzng he avaabe mehods o handng such daa ncude Fuer 987, Cheng and Van Ness 999 and Carro, Rupper and Seansk 006. An mporan dsncon beeen deren cases s based on ho he errors occur and ha her dsrbuon s. For eampe, an epanaory varabe canno be measured drecy or precsey, he vaues used n he sasca anayss are
4 u,,,, n, here n s he number o observaons. Deren assumpons can be made abou he so caed cassca measuremen errors u ; or eampe, hey are oen assumed o be ndependen and normay dsrbued h mean zero and varance,.e. u N 0,. u ~ u Hoever, hen he daa are coeced n a desgned epermen and he speced by he epermena desgn vaues o he h epanaory varabe are se h errors,.e. u,,,, n, he naccurae vaues are usuay used n he esmaon o he sasca mode o he daa because he vaues are no knon. he errors n hs case are knon as Berkson s errors, named aer Berkson 950 ho rs suded hs error srucure. In addon o he es noed above, here are aso many papers addressng ssues specc o he areas here he errors n varabes occur. he Fuer 987, p.79 dened he mng errors as an neresng probem o errors n varabes, her sudy appears med ony o hose presened by Sener and Hamada 997 and Hamada, Marz and Sener 005. hese researchers poned ou ha gnorng he mng errors eads o resus ha overesmae he varance o he response o neres and hence eads o ncreased condence nervas or he esmaes o he mode parameers and reduced poer o he sasca ess or her sgncance. hey proposed a Bayesan approach o esmae he parameers o he reured sasca modes or he daa, based on MCMC smuaons usng pror normaon abou he on dsrbuons o a mode parameers. hs emprca approach provdes a useu pracca oo or a beer sasca anayss han ha gnorng he mng errors, bu does no ao or esabshng a mporan eaures o he mpac o hese errors. 3
5 In hs paper e sudy he mpac o mng errors on he sasca anayss o he resus. ha makes he probem dcu s ha n desgned epermens h mures, hen here are mng errors, he errors made n seng he correc amouns o any ngreden, propagaes o he proporons reured by he epermena desgn or a ngredens. hereore he mng errors ead o a compe error srucure or he proporons o he mures. In Secon, e reve he man eaures o daa coeced n mure epermens and sho ho mng errors aec he resus he mng errors are gnored. As smpe ace desgns are reueny used n epermens h mures, e derve he bas n he esmaes o he mode parameers resung rom anayss ha gnores mng errors hen such desgns are used. he repor concudes h a dscusson abou he useuness o he presened resus.. Mure epermens h mng errors In a ypca sudy o a mure h componens, he epermener s neresed n he ay a response o neres, say y, depends on he proporons o he componens o he mure,,,,. Hence, 0 u,, here andu are oer and upper bounds or he proporon o he h componen n he mure. A mure h he desred proporons s obaned by mng approprae amouns,,,,, o he ngredens. In he absence o errors n seng he amouns o he mure componens, here s he oa amoun o / 4
6 he mure. hen 0 and u,,,,, he desgn regon s a reguar smpe hch has verces. Oen > 0 and u < or some or a o he mure componens. I he resung desgn regon agan has verces, ne varabes hch are near combnaons o he componens, caed pseudocomponens, can be dened n such a ay ha he reaonshps are sased or hese varabes. Hence, he probem can be redened as one or a reguar smpe desgn regon. Hoever, he consrans and u can be such ha he desgn regon s rreguar h a number o verces arger han. A comprehensve reve o resus reaed o epermens h mures s gven by Corne, 00. hen he amouns o he mure componens are se h errors, he acua amouns become X e, here e are he errors o seng he amouns o he h mure componen or he h observaon o he response. e assume ha e, or,,,, are ndependeny dsrbued random varabes h mean zero and varance,,,,, proporona o he dscharged amouns, here denes he ay he varance changes h he amoun. For eampe, can assumed ha. Hoever, hs assumpon has o be vered, usuay by a vadaon epermen. he mng errors can be a resu o echnca maons o he eupmen used n he epermen. hey can aso depend on he physca properes o he componens o he mure. For eampe, he componens are n ud orm, he errors n seng her amouns may depend on her vscosy, so ha he varances o he errors o seng he amouns or deren mure 5
7 componens may be deren, even he same eupmen s used o dscharge he reured amouns. Sandard poynomas canno be used o mode he ay he response depends on he mure proporons because o he consrans. Insead, oen he canonca poynomas proposed by Scheé 958 are used. For eampe, he rs and second order Scheé poynomas are y η, ε β β ε y, ε β η β β ε 3 respecvey, here β s a p vecor o a mode parameers and s a vecor o he proporons o he componens o he mure n he h observaon. e assume ha he response s measured h errors hch are normay dsrbued h zero mean and varance ε. Cusomary, smpe ace desgns are used hen he desgn regon s a reguar smpe, or pseudocomponens can be used o ransorm o an denca probem. In a {d, m} smpe-ace desgn, he proporons o each componen ake d euay spaced vaues rom 0 o, 0, /d, /d,...,, or,,...,. One advanage o hese desgns s ha he anayss o he daa and s nerpreaon s smped. For eampe, d s chosen o be eua o he order o Scheé poynoma ha be ed, he eas suares esmaors or he mode parameers o he rs and he second order Scheé poynomas are: βˆ y,,,, 4 6
8 and β ˆ 4y [ y y ],,,,, <, 5 here y denoes he average o he observaons hen he mure consss o he h componen ony, he y denoes he average o he observaons here he proporons o he mure o he h and he h componen are boh eua o 0.5. hen he desgn regon s rreguar, he desgn consrucon can be carred ou usng any o he desgn agorhms descrbed n Aknson e a. Chaper, 007. I ony he amoun o he h componen n he h observaon s se h error, he acua proporon o hs componen becomes e e, he he acua proporons o he remanng componens become. e e denoe he vecor o acua proporons,,...,. I he amouns o a mure componens are se h errors e k e k,,,...,. he error n he proporon o he h componen resung rom mng errors n a componens o he mure s u e e e k e k k k, 7
9 here k e k s he acua oa amoun. Ceary, he mure consss o a snge componen, as reured or some o he observaons o a smpe ace desgn h no consrans on he proporons o he componens, dschargng he rong amoun no change he reured proporon o hs componen,.e.. hereore he oong resus are concerned ony h cases here he mures conss o o or more componens. he mpac o he mng errors on he anayss o he daa s summarzed n he oong emmas. he resus o Lemmas and are obaned drecy by usng he dea mehod; or deas see Meyer 965, p.8. hereore her proos are no provded. Lemma. he epecaon and he varance o he acua proporon o he h componen o a mure n he h observaon, gven he arge proporon,,,,, are E[ ] var, respecvey. Lemma. he epecaon and he varance o he produc o he acua proporons and o he h and he h componens o a mure n he h observaon, gven he arge proporons and, are E 3 3 8
10 3. var 4 Lemmas and sho ha he means o boh he acua proporons and her producs are deren rom hose speced by he epermena desgn, and her varances ncrease h he vaues o he mode parameers. For eampe, n a smpe ace desgn, mng errors occur n he amouns o he componens o a bnary bend, here 0.5, and E. [ ] 0.5, [ ] 0.5 var 0.5. An mporan speca case s hen, as hen E ] [. hs means ha n hs case on average he arge amoun s acuay dscharged, and under some condons, he eec o mng errors coud be regarded neggbe. Hoever, n genera, he mng errors s aec he second order Scheé modes as [ ] 0.5 E, 9
11 he 0.5 and he modes become based. he eac mpac o he mng errors on he sasca anayss o he resus depends on he epermena desgn ha has been used and he sasca mode ha s esmaed. heorem. he mng errors make he mode based, ecep n he case hen he mure consss o a snge componen,.e. E[ y ] η β, B, here he bas B depends on he orm o he rue mode. he resu o hs heorem oos drecy rom Lemmas and. As usraon o hs heorem, he dervaon o he bas or he rs and second order Scheé poynoma modes s gven n he Append. heorem. he mng errors make he varance o he mode heerogeneous and arger han,.e. var y >. ε ε he resu o hs heorem oos by nong ha var y ε var B. he epresson or he varance o he response s very compe. hereore e ony sho s dervaon or he rs order Scheé poynoma mode n he Append. he mpac o he mng errors on he esmaes o he mode parameers hen he mng errors are gnored naïve esmaes depends on ha epermena desgn has been used n he sudy. Neverheess, s mporan o pon ou ha he esmaes o mode parameers are based, hs s because he epecaon o he response gven he 0
12 arge desgn s based. So, by anayzng he daa usng he proporons speced by he epermena desgn, he errors n proporons are ransmed o he error erm ε n he mode, causng E ε 0. e assume hou oss o generay ha a smpe ace desgn has been used. Lemmas and ao or ndng he correspondng resus hen oher epermena desgns are used. heorem 3. I daa coeced h a smpe ace desgn, he eas suares esmaors or he mode parameers are based, so ha E ˆ β β E ˆ β β [ ] β [ ] β β,,,,, <. he proo o hs heorem reures edous bu sraghorard agebra appyng he resu o heorem o mody he eas suares esmaors 4 and 5 and s omed. 3. Dscusson he resus presened n hs repor sho ha gnorng he mng errors usuay eads o aenuaon n he esmaes o mode parameers so ha he ordnary eas suares esmaes are based. he sze o he bas depends on many acors, bu many on he sze o he mng error varances. As a resu o he mng errors, he mode, hch may oherse be chosen correcy, becomes based and h ncreased heerogeneous varance. he speccaon o he orm o he bas s very mporan because aos or correcng or usng he regresson cabraon approach Carro and Seansk, 990.
13 An neresng appcaon o he presened resus be o use hem o devse suabe correcons o manuacurng sengs o mure producs hen errors n he dscharged amouns o he mure componens canno be avoded. hs s been subec o ongong research. Append Proo o heorem or he rs order Scheé poynoma mode I he amouns o a mure componens are dscharged h errors, he rue mode s y β ε, From Lemma, oos ha a naïve anayss o he daa gnorng he mng errors usng mode eads o predcons E[ y ] β β η β, Hence, he epeced response s based. B. Proo o heorem or he second order Scheé poynoma mode I a componens are measured h errors, he rue mode s gven by y β β ε. I oos rom Lemmas and ha E[ y ] β β B η β, B, here he bas s
14 B β β Proo o heorem or he rs order Scheé poynoma mode he varance o he response gven he desgn pons s, cov var var y β β β ε. Snce, appyng he resus o Lemmas and, gves ] [ ] [ ] [, cov E E E y var β ε 3 3 β β 3. Ceary he varance s arger han and depends on he proporon o he mure. ε Reerences Berkson, J Are here o Regressons? Journa o he Amercan Sasca Assocaon, 45, 50,
15 Carro, R.J., Seansk, L.A Appromae uas-kehood esmaon n modes h surrogae predcors. J. Amer. Sas. Assoc. 85, Carro, R., Rupper, D. and Seansk, L. A Measuremen Error n Nonnear Modes. nd edon, Chapman and Ha. Cheng, C. and Van Ness, J Sasca Regresson h Measuremen Errors. John ey & Sons, Ne York. Corne, J.A. 00 Epermens h mures: Desgn, Modes, and he Anayss o Mure Daa. 3rd Edon. ey, Ne York. Fuer,.A Measuremen Error Modes. John ey & Sons, Ne York. Meyer, P.L.965. Inroducory probaby and sasca appcaons. Addson- esey, Ne York. Scheé, H. 958 Epermens h mures. J.R.Sas.Soc. B, 0, Sener, S.H., Hamada, M Makng mures robus o nose and mng measuremen errors. Journa o Quay echnoogy, 9, 4, Hamada, M., Marz, H F., Sener S Accounng or Mure Errors n Anayzng Mure Epermens. Journa o Quay echnoogy, 37,,
Department of Economics University of Toronto
Deparmen of Economcs Unversy of Torono ECO408F M.A. Economercs Lecure Noes on Heeroskedascy Heeroskedascy o Ths lecure nvolves lookng a modfcaons we need o make o deal wh he regresson model when some of
More informationIn the complete model, these slopes are ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL. (! i+1 -! i ) + [(!") i+1,q - [(!
ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL The frs hng o es n wo-way ANOVA: Is here neracon? "No neracon" means: The man effecs model would f. Ths n urn means: In he neracon plo (wh A on he horzonal
More information( t) Outline of program: BGC1: Survival and event history analysis Oslo, March-May Recapitulation. The additive regression model
BGC1: Survval and even hsory analyss Oslo, March-May 212 Monday May 7h and Tuesday May 8h The addve regresson model Ørnulf Borgan Deparmen of Mahemacs Unversy of Oslo Oulne of program: Recapulaon Counng
More informationCHAPTER 7: CLUSTERING
CHAPTER 7: CLUSTERING Semparamerc Densy Esmaon 3 Paramerc: Assume a snge mode for p ( C ) (Chapers 4 and 5) Semparamerc: p ( C ) s a mure of denses Mupe possbe epanaons/prooypes: Dfferen handwrng syes,
More informationAppendix H: Rarefaction and extrapolation of Hill numbers for incidence data
Anne Chao Ncholas J Goell C seh lzabeh L ander K Ma Rober K Colwell and Aaron M llson 03 Rarefacon and erapolaon wh ll numbers: a framewor for samplng and esmaon n speces dversy sudes cology Monographs
More informationCHAPTER 10: LINEAR DISCRIMINATION
CHAPER : LINEAR DISCRIMINAION Dscrmnan-based Classfcaon 3 In classfcaon h K classes (C,C,, C k ) We defned dscrmnan funcon g j (), j=,,,k hen gven an es eample, e chose (predced) s class label as C f g
More informationLecture VI Regression
Lecure VI Regresson (Lnear Mehods for Regresson) Conens: Lnear Mehods for Regresson Leas Squares, Gauss Markov heorem Recursve Leas Squares Lecure VI: MLSC - Dr. Sehu Vjayakumar Lnear Regresson Model M
More informationCS434a/541a: Pattern Recognition Prof. Olga Veksler. Lecture 4
CS434a/54a: Paern Recognon Prof. Olga Veksler Lecure 4 Oulne Normal Random Varable Properes Dscrmnan funcons Why Normal Random Varables? Analycally racable Works well when observaon comes form a corruped
More informationV.Abramov - FURTHER ANALYSIS OF CONFIDENCE INTERVALS FOR LARGE CLIENT/SERVER COMPUTER NETWORKS
R&RATA # Vol.) 8, March FURTHER AALYSIS OF COFIDECE ITERVALS FOR LARGE CLIET/SERVER COMPUTER ETWORKS Vyacheslav Abramov School of Mahemacal Scences, Monash Unversy, Buldng 8, Level 4, Clayon Campus, Wellngon
More information12d Model. Civil and Surveying Software. Drainage Analysis Module Detention/Retention Basins. Owen Thornton BE (Mech), 12d Model Programmer
d Model Cvl and Surveyng Soware Dranage Analyss Module Deenon/Reenon Basns Owen Thornon BE (Mech), d Model Programmer owen.hornon@d.com 4 January 007 Revsed: 04 Aprl 007 9 February 008 (8Cp) Ths documen
More informationLecture 6: Learning for Control (Generalised Linear Regression)
Lecure 6: Learnng for Conrol (Generalsed Lnear Regresson) Conens: Lnear Mehods for Regresson Leas Squares, Gauss Markov heorem Recursve Leas Squares Lecure 6: RLSC - Prof. Sehu Vjayakumar Lnear Regresson
More informationRobustness Experiments with Two Variance Components
Naonal Insue of Sandards and Technology (NIST) Informaon Technology Laboraory (ITL) Sascal Engneerng Dvson (SED) Robusness Expermens wh Two Varance Componens by Ana Ivelsse Avlés avles@ns.gov Conference
More informationVariants of Pegasos. December 11, 2009
Inroducon Varans of Pegasos SooWoong Ryu bshboy@sanford.edu December, 009 Youngsoo Cho yc344@sanford.edu Developng a new SVM algorhm s ongong research opc. Among many exng SVM algorhms, we wll focus on
More informationNew M-Estimator Objective Function. in Simultaneous Equations Model. (A Comparative Study)
Inernaonal Mahemacal Forum, Vol. 8, 3, no., 7 - HIKARI Ld, www.m-hkar.com hp://dx.do.org/.988/mf.3.3488 New M-Esmaor Objecve Funcon n Smulaneous Equaons Model (A Comparave Sudy) Ahmed H. Youssef Professor
More informationStochastic State Estimation and Control for Stochastic Descriptor Systems
Sochasc Sae smaon and Conro for Sochasc Descrpor Sysems hwe Gao and aoyan Sh Schoo of ecrc and ecronc ngneerng ann Unversy ann 372, Chna e-ma: zhwegac@pubc.p..cn bsrac In hs paper, a sochasc observer s
More informationComputing Relevance, Similarity: The Vector Space Model
Compung Relevance, Smlary: The Vecor Space Model Based on Larson and Hears s sldes a UC-Bereley hp://.sms.bereley.edu/courses/s0/f00/ aabase Managemen Sysems, R. Ramarshnan ocumen Vecors v ocumens are
More information[Link to MIT-Lab 6P.1 goes here.] After completing the lab, fill in the following blanks: Numerical. Simulation s Calculations
Chaper 6: Ordnary Leas Squares Esmaon Procedure he Properes Chaper 6 Oulne Cln s Assgnmen: Assess he Effec of Sudyng on Quz Scores Revew o Regresson Model o Ordnary Leas Squares () Esmaon Procedure o he
More informationEcon107 Applied Econometrics Topic 5: Specification: Choosing Independent Variables (Studenmund, Chapter 6)
Econ7 Appled Economercs Topc 5: Specfcaon: Choosng Independen Varables (Sudenmund, Chaper 6 Specfcaon errors ha we wll deal wh: wrong ndependen varable; wrong funconal form. Ths lecure deals wh wrong ndependen
More informationRELATIONSHIP BETWEEN VOLATILITY AND TRADING VOLUME: THE CASE OF HSI STOCK RETURNS DATA
RELATIONSHIP BETWEEN VOLATILITY AND TRADING VOLUME: THE CASE OF HSI STOCK RETURNS DATA Mchaela Chocholaá Unversy of Economcs Braslava, Slovaka Inroducon (1) one of he characersc feaures of sock reurns
More informationMachine Learning Linear Regression
Machne Learnng Lnear Regresson Lesson 3 Lnear Regresson Bascs of Regresson Leas Squares esmaon Polynomal Regresson Bass funcons Regresson model Regularzed Regresson Sascal Regresson Mamum Lkelhood (ML)
More informationRelative controllability of nonlinear systems with delays in control
Relave conrollably o nonlnear sysems wh delays n conrol Jerzy Klamka Insue o Conrol Engneerng, Slesan Techncal Unversy, 44- Glwce, Poland. phone/ax : 48 32 37227, {jklamka}@a.polsl.glwce.pl Keywor: Conrollably.
More informationTHE POLYNOMIAL TENSOR INTERPOLATION
Pease ce hs arce as: Grzegorz Berna, Ana Ceo, The oynoma ensor neroaon, Scenfc Research of he Insue of Mahemacs and Comuer Scence, 28, oume 7, Issue, ages 5-. The webse: h://www.amcm.cz./ Scenfc Research
More informationDEEP UNFOLDING FOR MULTICHANNEL SOURCE SEPARATION SUPPLEMENTARY MATERIAL
DEEP UNFOLDING FOR MULTICHANNEL SOURCE SEPARATION SUPPLEMENTARY MATERIAL Sco Wsdom, John Hershey 2, Jonahan Le Roux 2, and Shnj Waanabe 2 Deparmen o Elecrcal Engneerng, Unversy o Washngon, Seale, WA, USA
More informationProbabilistic Forecasting of Wind Power Ramps Using Autoregressive Logit Models
obablsc Forecasng of Wnd Poer Ramps Usng Auoregressve Log Models James W. Taylor Saїd Busness School, Unversy of Oford 8 May 5 Brunel Unversy Conens Wnd poer and ramps Condonal AR log (CARL) Condonal AR
More informationAdvanced time-series analysis (University of Lund, Economic History Department)
Advanced me-seres analss (Unvers of Lund, Economc Hsor Dearmen) 3 Jan-3 Februar and 6-3 March Lecure 4 Economerc echnues for saonar seres : Unvarae sochasc models wh Box- Jenns mehodolog, smle forecasng
More informationDITAN: A TOOL FOR OPTIMAL SPACE TRAJECTORY DESIGN
DITAN: A TOOL FOR OPTIMAL SPACE TRAJECTORY DESIGN Massmano Vase Deparmen o Aerospace Engneerng Gasgow Unversy Gasgow Ruedger Jehn ESA/ESOC Inroducon o DITAN Fna Remarks Agenda Oune DITAN (drec Inerpaneary
More informationCHAPTER 5: MULTIVARIATE METHODS
CHAPER 5: MULIVARIAE MEHODS Mulvarae Daa 3 Mulple measuremens (sensors) npus/feaures/arbues: -varae N nsances/observaons/eamples Each row s an eample Each column represens a feaure X a b correspons o he
More informationBandlimited channel. Intersymbol interference (ISI) This non-ideal communication channel is also called dispersive channel
Inersymol nererence ISI ISI s a sgnal-dependen orm o nererence ha arses ecause o devaons n he requency response o a channel rom he deal channel. Example: Bandlmed channel Tme Doman Bandlmed channel Frequency
More informationCHAPTER 2: Supervised Learning
HATER 2: Supervsed Learnng Learnng a lass from Eamples lass of a famly car redcon: Is car a famly car? Knowledge eracon: Wha do people epec from a famly car? Oupu: osve (+) and negave ( ) eamples Inpu
More informationJanuary Examinations 2012
Page of 5 EC79 January Examnaons No. of Pages: 5 No. of Quesons: 8 Subjec ECONOMICS (POSTGRADUATE) Tle of Paper EC79 QUANTITATIVE METHODS FOR BUSINESS AND FINANCE Tme Allowed Two Hours ( hours) Insrucons
More informationTools for Analysis of Accelerated Life and Degradation Test Data
Acceleraed Sress Tesng and Relably Tools for Analyss of Acceleraed Lfe and Degradaon Tes Daa Presened by: Reuel Smh Unversy of Maryland College Park smhrc@umd.edu Sepember-5-6 Sepember 28-30 206, Pensacola
More informationTSS = SST + SSE An orthogonal partition of the total SS
ANOVA: Topc 4. Orhogonal conrass [ST&D p. 183] H 0 : µ 1 = µ =... = µ H 1 : The mean of a leas one reamen group s dfferen To es hs hypohess, a basc ANOVA allocaes he varaon among reamen means (SST) equally
More informationAnalysis And Evaluation of Econometric Time Series Models: Dynamic Transfer Function Approach
1 Appeared n Proceedng of he 62 h Annual Sesson of he SLAAS (2006) pp 96. Analyss And Evaluaon of Economerc Tme Seres Models: Dynamc Transfer Funcon Approach T.M.J.A.COORAY Deparmen of Mahemacs Unversy
More informationPHYS 1443 Section 001 Lecture #4
PHYS 1443 Secon 001 Lecure #4 Monda, June 5, 006 Moon n Two Dmensons Moon under consan acceleraon Projecle Moon Mamum ranges and heghs Reerence Frames and relae moon Newon s Laws o Moon Force Newon s Law
More informationIncluding the ordinary differential of distance with time as velocity makes a system of ordinary differential equations.
Soluons o Ordnary Derenal Equaons An ordnary derenal equaon has only one ndependen varable. A sysem o ordnary derenal equaons consss o several derenal equaons each wh he same ndependen varable. An eample
More informationStandard Error of Technical Cost Incorporating Parameter Uncertainty
Sandard rror of echncal Cos Incorporang Parameer Uncerany Chrsopher Moron Insurance Ausrala Group Presened o he Acuares Insue General Insurance Semnar 3 ovember 0 Sydney hs paper has been prepared for
More informationABSTRACT KEYWORDS. Bonus-malus systems, frequency component, severity component. 1. INTRODUCTION
EERAIED BU-MAU YTEM ITH A FREQUECY AD A EVERITY CMET A IDIVIDUA BAI I AUTMBIE IURACE* BY RAHIM MAHMUDVAD AD HEI HAAI ABTRACT Frangos and Vronos (2001) proposed an opmal bonus-malus sysems wh a frequency
More informationEndogeneity. Is the term given to the situation when one or more of the regressors in the model are correlated with the error term such that
s row Endogeney Is he erm gven o he suaon when one or more of he regressors n he model are correlaed wh he error erm such ha E( u 0 The 3 man causes of endogeney are: Measuremen error n he rgh hand sde
More informationShort-term Load Forecasting Model for Microgrid Based on HSA-SVM
MATEC Web of Conferences 73 0007 (08) hps://do.org/0.05/maecconf/08730007 SMIMA 08 Shor-erm Load Forecasng Mode for Mcrogrd Based on HSA-SVM Han Aoyang * Yu Lao An Shuhua Zhang Zhsheng 3* Qngdao Eecrc
More informationNormal Random Variable and its discriminant functions
Noral Rando Varable and s dscrnan funcons Oulne Noral Rando Varable Properes Dscrnan funcons Why Noral Rando Varables? Analycally racable Works well when observaon coes for a corruped snle prooype 3 The
More informationJohn Geweke a and Gianni Amisano b a Departments of Economics and Statistics, University of Iowa, USA b European Central Bank, Frankfurt, Germany
Herarchcal Markov Normal Mxure models wh Applcaons o Fnancal Asse Reurns Appendx: Proofs of Theorems and Condonal Poseror Dsrbuons John Geweke a and Gann Amsano b a Deparmens of Economcs and Sascs, Unversy
More informationBayesian Inference of the GARCH model with Rational Errors
0 Inernaonal Conference on Economcs, Busness and Markeng Managemen IPEDR vol.9 (0) (0) IACSIT Press, Sngapore Bayesan Inference of he GARCH model wh Raonal Errors Tesuya Takash + and Tng Tng Chen Hroshma
More informationRobustness of DEWMA versus EWMA Control Charts to Non-Normal Processes
Journal of Modern Appled Sascal Mehods Volume Issue Arcle 8 5--3 Robusness of D versus Conrol Chars o Non- Processes Saad Saeed Alkahan Performance Measuremen Cener of Governmen Agences, Insue of Publc
More informationShould Exact Index Numbers have Standard Errors? Theory and Application to Asian Growth
Should Exac Index umbers have Sandard Errors? Theory and Applcaon o Asan Growh Rober C. Feensra Marshall B. Rensdorf ovember 003 Proof of Proposon APPEDIX () Frs, we wll derve he convenonal Sao-Vara prce
More informationAdvanced Machine Learning & Perception
Advanced Machne Learnng & Percepon Insrucor: Tony Jebara SVM Feaure & Kernel Selecon SVM Eensons Feaure Selecon (Flerng and Wrappng) SVM Feaure Selecon SVM Kernel Selecon SVM Eensons Classfcaon Feaure/Kernel
More informationNPTEL Project. Econometric Modelling. Module23: Granger Causality Test. Lecture35: Granger Causality Test. Vinod Gupta School of Management
P age NPTEL Proec Economerc Modellng Vnod Gua School of Managemen Module23: Granger Causaly Tes Lecure35: Granger Causaly Tes Rudra P. Pradhan Vnod Gua School of Managemen Indan Insue of Technology Kharagur,
More informationA New Excitation Control for Multimachine Power Systems II: Robustness and Disturbance Attenuation Analysis
88 Inernaona Journa of Conro Hars Auomaon E Psaks and and Sysems Anono vo T Aexandrds no (speca edon) pp 88-95 June 5 A New Excaon Conro for umachne Power Sysems II: Robusness and Dsurbance Aenuaon Anayss
More informationKayode Ayinde Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology P. M. B. 4000, Ogbomoso, Oyo State, Nigeria
Journal of Mahemacs and Sascs 3 (4): 96-, 7 ISSN 549-3644 7 Scence Publcaons A Comparave Sudy of he Performances of he OLS and some GLS Esmaors when Sochasc egressors are boh Collnear and Correlaed wh
More informationMath 128b Project. Jude Yuen
Mah 8b Proec Jude Yuen . Inroducon Le { Z } be a sequence of observed ndependen vecor varables. If he elemens of Z have a on normal dsrbuon hen { Z } has a mean vecor Z and a varancecovarance marx z. Geomercally
More informationThe Research of Algorithm for Data Mining Based on Fuzzy Theory
The Research of Agorhm for Daa Mnng Based on Fuzzy Theory Wang Amn, L Je, Schoo of Compuer and Informaon Engneerng Anyang Norma Unversy Anyang, Chna Shenyang Insue of Compung Technoogy Chnese Academy of
More informationF-Tests and Analysis of Variance (ANOVA) in the Simple Linear Regression Model. 1. Introduction
ECOOMICS 35* -- OTE 9 ECO 35* -- OTE 9 F-Tess and Analyss of Varance (AOVA n he Smple Lnear Regresson Model Inroducon The smple lnear regresson model s gven by he followng populaon regresson equaon, or
More informationSurvival Analysis and Reliability. A Note on the Mean Residual Life Function of a Parallel System
Communcaons n Sascs Theory and Mehods, 34: 475 484, 2005 Copyrgh Taylor & Francs, Inc. ISSN: 0361-0926 prn/1532-415x onlne DOI: 10.1081/STA-200047430 Survval Analyss and Relably A Noe on he Mean Resdual
More informationThe Performance of Optimum Response Surface Methodology Based on MM-Estimator
The Performance of Opmum Response Surface Mehodology Based on MM-Esmaor Habshah Md, Mohd Shafe Musafa, Anwar Frano Absrac The Ordnary Leas Squares (OLS) mehod s ofen used o esmae he parameers of a second-order
More informationA HIERARCHICAL KALMAN FILTER
A HIERARCHICAL KALMAN FILER Greg aylor aylor Fry Consulng Acuares Level 8, 3 Clarence Sree Sydney NSW Ausrala Professoral Assocae, Cenre for Acuaral Sudes Faculy of Economcs and Commerce Unversy of Melbourne
More informationMethods of Improving Constitutive Equations
Mehods o mprovng Consuve Equaons Maxell Model e an mprove h ne me dervaves or ne sran measures. ³ ª º «e, d» ¼ e an also hange he bas equaon lnear modaons non-lnear modaons her Consuve Approahes Smple
More informationON THE WEAK LIMITS OF SMOOTH MAPS FOR THE DIRICHLET ENERGY BETWEEN MANIFOLDS
ON THE WEA LIMITS OF SMOOTH MAPS FOR THE DIRICHLET ENERGY BETWEEN MANIFOLDS FENGBO HANG Absrac. We denfy all he weak sequenal lms of smooh maps n W (M N). In parcular, hs mples a necessary su cen opologcal
More informationACEI working paper series RETRANSFORMATION BIAS IN THE ADJACENT ART PRICE INDEX
ACEI workng paper seres RETRANSFORMATION BIAS IN THE ADJACENT ART PRICE INDEX Andrew M. Jones Robero Zanola AWP-01-2011 Dae: July 2011 Reransformaon bas n he adjacen ar prce ndex * Andrew M. Jones and
More informationSingle-loop System Reliability-Based Design & Topology Optimization (SRBDO/SRBTO): A Matrix-based System Reliability (MSR) Method
10 h US Naonal Congress on Compuaonal Mechancs Columbus, Oho 16-19, 2009 Sngle-loop Sysem Relably-Based Desgn & Topology Opmzaon (SRBDO/SRBTO): A Marx-based Sysem Relably (MSR) Mehod Tam Nguyen, Junho
More informationStructural Optimization Using Metamodels
Srucural Opmzaon Usng Meamodels 30 Mar. 007 Dep. o Mechancal Engneerng Dong-A Unvers Korea Kwon-Hee Lee Conens. Numercal Opmzaon. Opmzaon Usng Meamodels Impac beam desgn WB Door desgn 3. Robus Opmzaon
More informationClustering with Gaussian Mixtures
Noe o oher eachers and users of hese sldes. Andrew would be delghed f you found hs source maeral useful n gvng your own lecures. Feel free o use hese sldes verbam, or o modfy hem o f your own needs. PowerPon
More informationLecture 16 (Momentum and Impulse, Collisions and Conservation of Momentum) Physics Spring 2017 Douglas Fields
Lecure 16 (Momenum and Impulse, Collisions and Conservaion o Momenum) Physics 160-02 Spring 2017 Douglas Fields Newon s Laws & Energy The work-energy heorem is relaed o Newon s 2 nd Law W KE 1 2 1 2 F
More informationAnomaly Detection. Lecture Notes for Chapter 9. Introduction to Data Mining, 2 nd Edition by Tan, Steinbach, Karpatne, Kumar
Anomaly eecon Lecure Noes for Chaper 9 Inroducon o aa Mnng, 2 nd Edon by Tan, Senbach, Karpane, Kumar 2/14/18 Inroducon o aa Mnng, 2nd Edon 1 Anomaly/Ouler eecon Wha are anomales/oulers? The se of daa
More informationOn One Analytic Method of. Constructing Program Controls
Appled Mahemacal Scences, Vol. 9, 05, no. 8, 409-407 HIKARI Ld, www.m-hkar.com hp://dx.do.org/0.988/ams.05.54349 On One Analyc Mehod of Consrucng Program Conrols A. N. Kvko, S. V. Chsyakov and Yu. E. Balyna
More informationTraining Algorithm of Adaptive Neural Fuzzy Inference System Based on Improved SRUKF
IAEG Inernaona Journa of Compuer Scence, 44:4, IJCS_44_4_ ranng Agorhm of Adapve eura Fuy Inference Sysem Based on Improved SRUKF Wang Hong and Gao onghu Absrac o sove he probem of ow predcon accuracy
More informationChapter 6 DETECTION AND ESTIMATION: Model of digital communication system. Fundamental issues in digital communications are
Chaper 6 DEECIO AD EIMAIO: Fundamenal ssues n dgal communcaons are. Deecon and. Esmaon Deecon heory: I deals wh he desgn and evaluaon of decson makng processor ha observes he receved sgnal and guesses
More information2. SPATIALLY LAGGED DEPENDENT VARIABLES
2. SPATIALLY LAGGED DEPENDENT VARIABLES In hs chaper, we descrbe a sascal model ha ncorporaes spaal dependence explcly by addng a spaally lagged dependen varable y on he rgh-hand sde of he regresson equaon.
More informationCOMPUTER SCIENCE 349A SAMPLE EXAM QUESTIONS WITH SOLUTIONS PARTS 1, 2
COMPUTE SCIENCE 49A SAMPLE EXAM QUESTIONS WITH SOLUTIONS PATS, PAT.. a Dene he erm ll-ondoned problem. b Gve an eample o a polynomal ha has ll-ondoned zeros.. Consder evaluaon o anh, where e e anh. e e
More informationMachine Learning 2nd Edition
INTRODUCTION TO Lecure Sldes for Machne Learnng nd Edon ETHEM ALPAYDIN, modfed by Leonardo Bobadlla and some pars from hp://www.cs.au.ac.l/~aparzn/machnelearnng/ The MIT Press, 00 alpaydn@boun.edu.r hp://www.cmpe.boun.edu.r/~ehem/mle
More informationPartitioned Multiprocessor Fixed-Priority Scheduling of Sporadic Real-Time Tasks
Paroned uprocessor Fxed-Prory Schedung o Sporadc Rea-Tme Tasks Jan-Ja Chen Deparmen o Inormacs, TU Dormund Unversy, Germany E-ma: jan-jachen@csun-dormundde To schedue rea-me asks on muprocessor paorms,
More informationA New Generalisation of Sam-Solai s Multivariate symmetric Arcsine Distribution of Kind-1*
IOSR Journal o Mahemacs IOSRJM ISSN: 78-578 Volume, Issue May-June 0, PP 4-48 www.osrournals.org A New Generalsaon o Sam-Sola s Mulvarae symmerc Arcsne Dsrbuon o Knd-* Dr. G.S. Davd Sam Jayaumar. Dr.A.Solarau.
More informationResearch on Complex Networks Control Based on Fuzzy Integral Sliding Theory
Advanced Scence and Technoogy Letters Vo.83 (ISA 205), pp.60-65 http://dx.do.org/0.4257/ast.205.83.2 Research on Compex etworks Contro Based on Fuzzy Integra Sdng Theory Dongsheng Yang, Bngqng L, 2, He
More informationNested case-control and case-cohort studies
Outne: Nested case-contro and case-cohort studes Ørnuf Borgan Department of Mathematcs Unversty of Oso NORBIS course Unversty of Oso 4-8 December 217 1 Radaton and breast cancer data Nested case contro
More informationChapter 6 DETECTION AND ESTIMATION: Model of digital communication system. Fundamental issues in digital communications are
Chaper 6 DCIO AD IMAIO: Fndaenal sses n dgal concaons are. Deecon and. saon Deecon heory: I deals wh he desgn and evalaon of decson ang processor ha observes he receved sgnal and gesses whch parclar sybol
More informationSparse Kernel Ridge Regression Using Backward Deletion
Sparse Kerne Rdge Regresson Usng Backward Deeon Lng Wang, Lefeng Bo, and Lcheng Jao Insue of Inegen Informaon Processng 710071, Xdan Unversy, X an, Chna {wp, bf018}@163.com Absrac. Based on he feaure map
More informationCS286.2 Lecture 14: Quantum de Finetti Theorems II
CS286.2 Lecure 14: Quanum de Fne Theorems II Scrbe: Mara Okounkova 1 Saemen of he heorem Recall he las saemen of he quanum de Fne heorem from he prevous lecure. Theorem 1 Quanum de Fne). Le ρ Dens C 2
More informationOrdinary Differential Equations in Neuroscience with Matlab examples. Aim 1- Gain understanding of how to set up and solve ODE s
Ordnary Dfferenal Equaons n Neuroscence wh Malab eamples. Am - Gan undersandng of how o se up and solve ODE s Am Undersand how o se up an solve a smple eample of he Hebb rule n D Our goal a end of class
More informationSparse Kernel Ridge Regression Using Backward Deletion
Sparse Kerne Rdge Regresson Usng Bacward Deeon Lng Wang, Lefeng Bo, and Lcheng Jao Insue of Inegen Informaon Processng 7007, Xdan Unversy, X an, Chna {wp, bf08}@63.com Absrac. Based on he feaure map prncpe,
More informationTHEORETICAL AUTOCORRELATIONS. ) if often denoted by γ. Note that
THEORETICAL AUTOCORRELATIONS Cov( y, y ) E( y E( y))( y E( y)) ρ = = Var( y) E( y E( y)) =,, L ρ = and Cov( y, y ) s ofen denoed by whle Var( y ) f ofen denoed by γ. Noe ha γ = γ and ρ = ρ and because
More informationComparison of Alternative Labour Force Survey Estimators
Surve Mehodolog, June 2001 53 Vol. 27, No. 1, pp. 53 63 Sascs Canada, Caalogue No. 12 001 Comparson of Alernave Labour Force Surve Esmaors Phlp ell 1 Absrac Ths paper loos a a range of esmaors applcable
More informationHEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD
Journal of Appled Mahemacs and Compuaonal Mechancs 3, (), 45-5 HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD Sansław Kukla, Urszula Sedlecka Insue of Mahemacs,
More informationCHAPTER FOUR REPEATED MEASURES IN TOXICITY TESTING
CHAPTER FOUR REPEATED MEASURES IN TOXICITY TESTING 4. Inroducon The repeaed measures sudy s a very commonly used expermenal desgn n oxcy esng because no only allows one o nvesgae he effecs of he oxcans,
More informationPanel Data Regression Models
Panel Daa Regresson Models Wha s Panel Daa? () Mulple dmensoned Dmensons, e.g., cross-secon and me node-o-node (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy (c) Pongsa Pornchawseskul,
More informationClustering (Bishop ch 9)
Cluserng (Bshop ch 9) Reference: Daa Mnng by Margare Dunham (a slde source) 1 Cluserng Cluserng s unsupervsed learnng, here are no class labels Wan o fnd groups of smlar nsances Ofen use a dsance measure
More informationOnline Appendix for. Strategic safety stocks in supply chains with evolving forecasts
Onlne Appendx for Sraegc safey socs n supply chans wh evolvng forecass Tor Schoenmeyr Sephen C. Graves Opsolar, Inc. 332 Hunwood Avenue Hayward, CA 94544 A. P. Sloan School of Managemen Massachuses Insue
More informationOn Kalman Information Fusion for Multiple Wireless Sensors Networks Systems with Multiplicative Noise
Sensors & ransducers Vo. 76 Issue 8 Auus 04 pp. 5764 Sensors & ransducers 04 b IFSA Pubshn S. L. hp://www.sensorspora.com On Kaman Informaon Fuson for Mupe Wreess Sensors Neworks Ssems wh Mupcave Nose
More informationFirst-order piecewise-linear dynamic circuits
Frs-order pecewse-lnear dynamc crcus. Fndng he soluon We wll sudy rs-order dynamc crcus composed o a nonlnear resse one-por, ermnaed eher by a lnear capacor or a lnear nducor (see Fg.. Nonlnear resse one-por
More informationFall 2009 Social Sciences 7418 University of Wisconsin-Madison. Problem Set 2 Answers (4) (6) di = D (10)
Publc Affars 974 Menze D. Chnn Fall 2009 Socal Scences 7418 Unversy of Wsconsn-Madson Problem Se 2 Answers Due n lecure on Thursday, November 12. " Box n" your answers o he algebrac quesons. 1. Consder
More informationMatlab and Python programming: how to get started
Malab and Pyhon programming: how o ge sared Equipping readers he skills o wrie programs o explore complex sysems and discover ineresing paerns from big daa is one of he main goals of his book. In his chaper,
More informationS. J. Sadjadi*, Mir.B.Gh. Aryanezhad & H.A. Sadeghi
Inernaona Journa o Indusra Engneerng & Producon Research (009) pp. ecember 009, Voume 0, Number Inernaona Journa o Indusra Engneerng & Producon Research ISSN: 008889 Journa Webse: hp://ijiepr.us.ac.r/
More informationRobust Output Tracking of Uncertain Large-Scale Input-Delay Systems via Decentralized Fuzzy Sliding Mode Control
Inernaona Journa of Conro Scence and Engneerng (6: 57-7 DOI:.593/.conro.6.4 Robus Oupu rackng of Unceran Large-Scae Inpu-Deay Sysems va Decenrazed Fuzzy Sdng Mode Conro Chang-Che ng Chang Deparmen of Eecrca
More informationPhD/MA Econometrics Examination. January, 2019
Economercs Comprehensve Exam January 2019 Toal Tme: 8 hours MA sudens are requred o answer from A and B. PhD/MA Economercs Examnaon January, 2019 PhD sudens are requred o answer from A, B, and C. The answers
More informationOptimal Pollution Tax in Cournot Oligopsonistic Oligopoly
Oma Pouon Tax n Courno Oosonsc Ooo Ko Okuuch Dearmen o Economcs and Inormaon Gu Shooku Gakuen Unvers 1-38 NakauzuraGu-shGu-ken 5-888Jaan E-ma:okuuch@u.shooku.ac. Absrac The oma ouon ax rae hch maxmzes
More informationThe Shapley value for fuzzy games on vague sets
WEA TRANACTIN on INFRMATIN CIENCE APPLICATIN The hapley value or uzzy games on vague ses Fan-Yong Meng* (Correspondng Auhor chool o Managemen Qngdao Technologcal nversy Qngdao 266520 hong Provnce P R Chna
More informationBayes rule for a classification problem INF Discriminant functions for the normal density. Euclidean distance. Mahalanobis distance
INF 43 3.. Repeon Anne Solberg (anne@f.uo.no Bayes rule for a classfcaon problem Suppose we have J, =,...J classes. s he class label for a pxel, and x s he observed feaure vecor. We can use Bayes rule
More informationCubic Bezier Homotopy Function for Solving Exponential Equations
Penerb Journal of Advanced Research n Compung and Applcaons ISSN (onlne: 46-97 Vol. 4, No.. Pages -8, 6 omoopy Funcon for Solvng Eponenal Equaons S. S. Raml *,,. Mohamad Nor,a, N. S. Saharzan,b and M.
More informationCH.3. COMPATIBILITY EQUATIONS. Continuum Mechanics Course (MMC) - ETSECCPB - UPC
CH.3. COMPATIBILITY EQUATIONS Connuum Mechancs Course (MMC) - ETSECCPB - UPC Overvew Compably Condons Compably Equaons of a Poenal Vecor Feld Compably Condons for Infnesmal Srans Inegraon of he Infnesmal
More informationFall 2010 Graduate Course on Dynamic Learning
Fall 200 Graduae Course on Dynamc Learnng Chaper 4: Parcle Flers Sepember 27, 200 Byoung-Tak Zhang School of Compuer Scence and Engneerng & Cognve Scence and Bran Scence Programs Seoul aonal Unversy hp://b.snu.ac.kr/~bzhang/
More informationSolution in semi infinite diffusion couples (error function analysis)
Soluon n sem nfne dffuson couples (error funcon analyss) Le us consder now he sem nfne dffuson couple of wo blocks wh concenraon of and I means ha, n a A- bnary sysem, s bondng beween wo blocks made of
More informationChapter 8 Dynamic Models
Chaper 8 Dnamc odels 8. Inroducon 8. Seral correlaon models 8.3 Cross-seconal correlaons and me-seres crosssecon models 8.4 me-varng coeffcens 8.5 Kalman fler approach 8. Inroducon When s mporan o consder
More informationThe Finite Element Method for the Analysis of Non-Linear and Dynamic Systems
Swss Federal Insue of Page 1 The Fne Elemen Mehod for he Analyss of Non-Lnear and Dynamc Sysems Prof. Dr. Mchael Havbro Faber Dr. Nebojsa Mojslovc Swss Federal Insue of ETH Zurch, Swzerland Mehod of Fne
More information