On the Restricted Almost Unbiased Ridge Estimator in Logistic Regression
|
|
- Lauren Robertson
- 5 years ago
- Views:
Transcription
1 Open Journal of Statstcs, 06, 6, ISSN Onlne: ISSN Prnt: 6-78X On the Restrcted Almost Unbased Rdge Estmator n Logstc Regresson Nagarajah Varathan,, Pushpaanthe Wjeoon 3 Postgraduate Insttute of Scence, Unversty of Peradenya, Peradenya, Sr Lana Department of Mathematcs and Statstcs, Unversty of Jaffna, Jaffna, Sr Lana 3 Department of Statstcs and Computer Scence, Unversty of Peradenya, Peradenya, Sr Lana How to cte ths paper: Varathan, N. and Wjeoon, P. (06) On the Restrcted Almost Unbased Rdge Estmator n Logstc Regresson. Open Journal of Statstcs, 6, Receved: September 0, 06 Accepted: December 3, 06 Publshed: December 8, 06 Copyrght 06 by authors and Scentfc Research Publshng Inc. Ths wor s lcensed under the Creatve Commons Attrbuton Internatonal Lcense (CC BY 4.0). Open Access Abstract In ths artcle, the restrcted almost unbased rdge logstc estmator (RAURLE) s proposed to estmate the parameter n a logstc regresson model wth exact lnear restrctons when there exsts multcollnearty among explanatory varables. The performance of the proposed estmator over the maxmum lelhood estmator (), rdge logstc estmator (RLE), almost unbased rdge logstc estmator (AURLE), and restrcted maxmum lelhood estmator (R) wth respect to dfferent rdge parameters s nvestgated through a smulaton study n terms of scalar mean square error. Keywords Multcollnearty, Rdge Estmator, Almost Unbased Rdge Logstc Estmator, Lnear Restrctons, Scalar Mean Square Error. Introducton Multcollnearty nflates the varance of the maxmum lelhood estmator () n the logstc regresson. As a result, one may not obtan an effcent estmate for the parameter β n the logstc regresson model. To combat the multcollnearty n logstc regresson, several alternatve technques have been proposed n the lterature. One of the most famous technques s to consder sutable based estmators n place of Maxmum lelhood estmator. The based estmators proposed n the lterature, are the Rdge Logstc Estmator (RLE) (Schaefer et al., 984 []), Lu Logstc Estmator (LLE) (Lu, 993 [], Urgan and Tez, 008 [3], and Mansson et al., 0 [4]), Prncpal Component Logstc Estmator (PCLE) (Agulera et al., 006 [5]), Modfed Logstc Rdge Estmator (MLRE) (Nja et al., 03 [6]), Lu-type estmator (Inan and Erdogan, 03 DOI: 0.436/ojs December 8, 06
2 N. Varathan, P. Wjeoon [7]), and Almost Unbased Lu Logstc Estmator (AULLE) (Xnfeng, 05 [8]). Morever, Asar (05) [9], proposed some new methods to solve the multcollnearty n logstc regresson by ntroducng new methods of estmatng the shrnage parameter n Lu-type estmators. Only the sample nformaton was used n all the above estmaton procedures. An alternatve technque suggested to solve the multcollnearty problem s to consder parameter estmaton wth some lnear restrctons on the unnown parameters, whch are generally based on pror nformaton of the sample data, and further they may be n the exact or stochastc form. By ncorporatng lnear restrctons to the sample nformaton, dfferent types of based estmators were ntroduced n the lterature, and some researchers have ncorporated these estmators wth the logstc regresson estmator to mprove ts performance. In the presence of exact lnear restrctons n addton to sample logstc regresson model, Duffy and Santer (989) [0] ntroduced the restrcted maxmum lelhood estmator (R) by ncorporatng the restrcted least squares estmator based on exact lnear restrcton to the logstc regresson. Later, the Restrcted Logstc Rdge Estmator (Asar et al., 06 []), Restrcted Logstc Lu Estmator (RLLE) (Şray et al., 05 []), Modfed Restrcted Lu Estmator (Wu, 06 [3]), Restrcted two parameter Lu type estmator (Asar et al., 06 [4]) were ntroduced to the logstc regresson wth exact lnear restrctons. In the presence of stochastc lnear restrctons n addton to sample logstc regresson model, Nagarajah and Wjeoon (05) ntroduced the Stochastc Restrcted Maxmum Lelhood Estmator (SR). Followng Nagarajah and Wjeoon (05) [5], the Stochastc Restrcted Rdge Maxmum Lelhood Estmator (SRR) was proposed by Varathan and Wjeoon (06) [6] by ncorporatng Rdge Logstc Estmator (RLE) wth the SR. Wu and Asar (06) [7] has proposed a new based estmator called Almost Unbased Rdge Logstc Estmator (AURLE), and shown ts performance over the other avalable estmators. In ths artcle, we further mprove the logstc regresson estmator by combnng AURLE wth R, and name t as the Restrcted Almost Unbased Rdge Logstc Estmator (RAURLE). Further, the performance of RAURLE based on estmated rdge parameters usng dfferent methods gven n the lterature was consdered, and compared each of these cases wth, RLE, AURLE and R. The proceedng sectons of the artcle are organzed as follows. The model specfcaton and estmaton are dscussed n Secton. The proposed estmator and ts asymptotc propertes are gven n Secton 3. Secton 4 descrbes the exstng methods related to some rdge parameters. In Secton 5, the performance of the proposed estmator by consderng dfferent rdge parameters s compared wth respect to the scalar mean squared error (SMSE) wth, RLE, AURLE and R by performng a Monte Carlo smulaton study. Fnally, conclusons of the study are presented n Secton 6.. Model Specfcaton and Estmaton Consder the followng logstc regresson model y π + ε,,, n () 077
3 N. Varathan, P. Wjeoon whch follows Bernoull dstrbuton wth parameter exp π + exp ( x β ) ( x β ), π as where x s the th row of X, whch s an n ( p ) varables and β s a ( p + ) vector of coeffcents, zero and varance π( π) of the response () of β can be obtaned as follows:, () + data matrx wth p predctor ε are ndependent wth mean y. The maxmum lelhood estmator β C X WZ (3) where C X WX ; Z s the column vector wth th element equals y π logt ( π ) + and W dag π ( π) π π, whch s an unbased estmate of ( ) β. The covarance matrx of β s Cov ( β ) { } X WX. (4) In the presence of multcollnearty, Schaefer et al. (984) [] proposed to ncorporate the Logstc Rdge Estmator (LRE), n place of the n the logstc regresson model () ( ) ( ) LRE X WX I X WX C I C Z β + β + β β (5) where ( ) Z C + I C and s the rdge parameter, 0. The asymptotc propertes of LRE: E β LRE E Zβ Zβ Cov β LRE Cov Z β ZC Z ( C I ) C ( C I ) Z ( C I ) However the LRE s a based estmator whch produces nconsstent estmates for the parameter (Wu and Asar, 06 [7]). Consequently, the Almost Unbased Rdge Logstc Estmator (AURLE) was ntroduced by Wu and Asar (06) [7] and t s defned as where ( ) ( ) β β β F I X WX + I. AURLE I X WX + I F And the asymptotc propertes of AURLE: E β AURLE E F β F β Cov β AURLE Cov F β F C F As another remedal acton for multcollnearty, one may use the exact lnear restrctons n addton to the sample logstc regresson model (). The resultng est- mator s called as Restrcted estmator. (6) (7) (8) (9) (0) 078
4 N. Varathan, P. Wjeoon Suppose that the followng exact restrcton s gven n addton to the general logstc regresson model (). Hβ h () where H s a ( q ( p+ ) ) nown matrx and h s an ( ) q vector of nown con- stants. In the presence of the above restrcton () n addton to the logstc regresson model (), Duffy and Santner (989) [0] proposed the followng Restrcted Maxmum Lelhood Estmator (R). ( ) ( ) R β β C H HC H Hβ h () The asymptotc mean and varance of R β are ( ) ( ) E β R E β C H HC H Hβ h ( ) ( β ) β C H HC H H h (3) and Consequently the bas of ( ) ( β ) R ( ) Cov C C H HC H HC A say. (4) R β, 3. The Proposed Estmator ( βr ) ( ) ( β ) Bas C H HC H H h. (5) To mprove the performance of the estmators further, n ths secton, by combnng AURLE and R, we propose a new estmator whch s called as the Restrcted Almost Unbased Rdge Logstc Estmator (RAURLE) and defned as ( ) β RAURLE I X WX + I βr F β R (6) where F ( ) I X WX + I. Note that ths estmator s based on the rdge parameter, and ts performance s based on the choce of. The asymptotc propertes of RAURLE β are E β RAURLE E F β R F β C H ( HC H ) ( Hβ h), (7) and ( ) ( ) ( ) ( ) D β Cov β Cov F β F Cov β F F AF, (8) RAURLE RAURLE R R ( βraurle ) β RAURLE β β ( ) ( β ) β δ ( ) Bas E F C H HC H H h say.(9) Consequently, the mean square error can be obtaned as, ( ) ( ) ( ) ( ) MSE β D β + Bas β Bas β F AF + δδ (0) RAURLE RAURLE RAURLE RAURLE 079
5 N. Varathan, P. Wjeoon 4. Some Rdge Estmators Now we consder the exstng methods to obtan an estmated value for the rdge parameter, snce RAURLE depends on. Many researchers suggested varous methods of estmatng the rdge parameter n the rdge regresson approach and recently ths estmaton method s added to the logstc regresson. In ths research, we have consdered the followng exstng rdge parameter estmaton methods to compare the performance of the proposed estmator wth some exstng estmators n logstc regresson. ) Hoerl and Kennard (970) [8]; HK σ () α where α max s the maxmum element of γβ, γ s the egen vector of X WX. ) Hoerl et al. (975) [9]; HKB max where p s the number of predctor varables n the model (). 3) Lawless and Wang (976) [0]; LW p σ () β β p σ (3) β X WX β 4) Lndley and Smth (97) []; LS ( )( + ) ( n ) n p p p σ + β β (4) 5) Schaefer et al. (984) []; 5. Smulaton Study HK (5) α max It s dffcult to compare the mean square error of the estmators theoretcally, snce none of the estmators, RLE, AURLE, R and RAURLE are not always superor. So, we use Monte Carlo smulaton to examne the performance of the proposed estmator over the exstng estmators under dfferent levels of multcollnearty. Followng McDonald and Galarneau (975) [] and Kbra (003) [3], the explanatory varables are generated usng the followng equaton. ( ) xj ρ zj + ρ z, p+,,,, n, j,,, p (6) where z j are ndependent pseudo standard normal random numbers and ρ represents the correlaton between any two explanatory varables. The n observatons for the response varable are obtaned from the Bernoull ( π ) dstrbuton n (). Four explanatory varables are generated usng (6) and four dfferent values of ρ correspondng 080
6 N. Varathan, P. Wjeoon to 0.80, 0.90, 0.95 and 0.99 are consdered. Further for the sample sze n, three dfferent values 5, 60, and 00 are also consdered. The parameter values of β, β,, βp are p chosen so that β j j and β β βp, whch s common restrctons n many smulaton studes. Further for the rdge parameter, fve dfferent choces are used as defned n the Equatons ()-(5). The smulaton s repeated 000 tmes by generatng new pseudo-random numbers and the smulated SMSE values of the estmators are obtaned usng the followng equaton. 000 ( * ) ( SMSE β β ) ( r β βr β) (7) 000 where r β s any estmator consdered n the r th smulaton. The smulaton results are gven n Tables -3. It can be notced from the Tables -3 that the scalar mean square error of the proposed estmator RAURLE s smaller compared to, RLE, AURLE and R, wth respect to all the selected values of n, ρ, and, consdered n ths research. Further, the new estmator RAURLE has better performance when SRW s used. 6. Concludng Remars In ths paper, we proposed a restrcted almost unbased rdge logstc estmator (RAURLE) n logstc regresson wth exact lnear restrctons when the explanatory varables are hghly correlated. Through a Monte Carlo smulaton study, we examned r Table. The estmated SMSE values for dfferent, when n 5. ρ Estmator HK SRW HKB LW LS RLE AURLE R RAURLE RLE AURLE R RAURLE RLE AURLE R RAURLE RLE AURLE R RAURLE
7 N. Varathan, P. Wjeoon Table. The estmated SMSE values for dfferent, when n 60. ρ Estmator HK SRW HKB LW LS RLE AURLE R RAURLE RLE AURLE R RAURLE RLE AURLE R RAURLE RLE AURLE R RAURLE Table 3. The estmated SMSE values for dfferent, when n 00. ρ Estmator HK SRW HKB LW LS RLE AURLE R RAURLE RLE AURLE R RAURLE RLE AURLE R RAURLE RLE AURLE R RAURLE
8 N. Varathan, P. Wjeoon the performance of the proposed estmator over some exstng estmators, RLE, AURLE and R n terms of scalar mean square error. Also, fve dfferent choces of exstng rdge parameter estmates were used to compare the estmators. The results show that the newly proposed estmator outperforms all the other estmators consdered n ths study under the selected values of n, ρ, and by means of SMSE. Acnowledgements We than the Edtor and the referee for ther comments and suggestons, and the Postgraduate Insttute of Scence, Unversty of Peradenya, Sr Lana for provdng necessary facltes to complete ths research. References [] Schaefer, R.L., Ro, L.D. and Wolfe, R.A. (984) A Rdge Logstc Estmator. Communcatons n Statstcs - Theory and Methods, 3, [] Lu, K. (993) A New Class of Based Estmate n Lnear Regresson. Communcatons n Statstcs - Theory and Methods,, [3] Urgan, N.N. and Tez, M. (008) Lu Estmator n Logstc Regresson When the Data Are Collnear. Internatonal Conference. Contnuous Optmzaton and Knowledge-Based Technologes, [4] Mansson, G., Kbra, B.M.G. and Shuur, G. (0) On Lu Estmators for the Logt Regresson Model. The Royal Insttute of Techonology, Centre of Excellence for Scence and Innovaton Studes (CESIS), Sweden, Paper No. 59. [5] Agulera, A.M., Escabas, M. and Valderrama, M.J. (006) Usng Prncpal Components for Estmatng Logstc Regresson wth Hgh-Dmensonal Multcollnear Data. Computatonal Statstcs & Data Analyss, 50, [6] Nja, M.E., Ogoe, U.P. and Ndua, E.C. (03) The Logstc Regresson Model wth a Modfed Weght Functon. Journal of Statstcal and Econometrc Method,, 6-7. [7] Inan, D. and Erdogan, B.E. (03) Lu-Type Logstc Estmator. Communcatons n Statstcs - Smulaton and Computaton, 4, [8] Xnfeng, C. (05) On the Almost Unbased Rdge and Lu Estmator n the Logstc Regresson Model. Internatonal Conference on Socal Scence, Educaton Management and Sports Educaton, Atlants Press, Amsterdam, [9] Asar, Y. (05) Some New Methods to Solve Multcollnearty n Logstc Regresson. Communcatons n Statstcs - Smulaton and Computaton, Onlne. [0] Duffy, D.E. and Santner, T.J. (989) On the Small Sample Prospertes of Norm-Restrcted Maxmum Lelhood Estmators for Logstc Regresson Models. Communcatons n Statstcs - Theory and Methods, 8, [] Asar, Y., Arash, M. and Wu, J. (06) Restrcted Rdge Estmator n the Logstc Regresson Model. Communcatons n Statstcs - Smulaton and Computaton, Onlne. [] Şray, G.U., Toer, S. and Kaçranlar, S. (05) On the Restrcted Lu Estmator n Logstc Regresson Model. Communcatons n Statstcs - Smulaton and Computaton, 44, 7-083
9 N. Varathan, P. Wjeoon 3. [3] Wu, J. (06) Modfed Restrcted Lu Estmator n Logstc Regresson Model. Computatonal Statstcs, 3, [4] Asar, Y., Erşoğlu, M. and Arash, M. (06) Developng a Restrcted Two Parameter Lu-Type Estmator: A Comparson of Restrcted Estmators n the Bnary Logstc Regresson Model. Communcatons n Statstcs - Theory and Methods, Onlne. [5] Nagarajah, V. and Wjeoon, P. (05) Stochastc Restrcted Maxmum Lelhood Estmator n Logstc Regresson Model. Open Journal of Statstcs, 5, [6] Varathan, N. and Wjeoon, P. (06) Rdge Estmator n Logstc Regresson under Stochastc Lnear Restrcton. Brtsh Journal of Mathematcs & Computer Scence, 5,. [7] Wu, J. and Asar, Y. (06) On Almost Unbased Rdge Logstc Estmator for the Logstc Regresson Model. Hacettepe Journal of Mathematcs and Statstcs, 45, [8] Hoerl, E. and Kennard, R.W. (970) Rdge Regresson: Based Estmaton for Nonorthogonal Problems. Technometrcs,, [9] Hoerl, E., Kennard, R.W. and Baldwn, K.F. (975) Rdge Regresson: Some Smulatons. Communcatons n Statstcs, 4, [0] Lawless, J.F. and Wang, P. (976) A Smulaton Study of Rdge and Other Regresson Estmators. Communcatons n Statstcs - Theory and Methods, 4, [] Lndley, D.V. and Smth, A.F.M. (97) Bayes Estmate for the Lnear Model (wth Dscusson) Part. Journal of the Royal Statstcal Socety, Ser B, 34, -4. [] McDonald, G.C. and Galarneau, D.I. (975) A Monte Carlo Evaluaton of Some Rdge-Type Estmators. Journal of the Amercan Statstcal Assocaton, 70, [3] Kbra, B.M.G. (003) Performance of Some New Rdge Regresson Estmators. Communcatons n Statstcs - Theory and Methods, 3,
10 Submt or recommend next manuscrpt to SCIRP and we wll provde best servce for you: Acceptng pre-submsson nqures through Emal, Faceboo, LnedIn, Twtter, etc. A wde selecton of journals (nclusve of 9 subjects, more than 00 journals) Provdng 4-hour hgh-qualty servce User-frendly onlne submsson system Far and swft peer-revew system Effcent typesettng and proofreadng procedure Dsplay of the result of downloads and vsts, as well as the number of cted artcles Maxmum dssemnaton of your research wor Submt your manuscrpt at: Or contact ojs@scrp.org
Stochastic Restricted Maximum Likelihood Estimator in Logistic Regression Model
Open Journal of Statstcs, 05, 5, 837-85 Publshed Onlne December 05 n ScRes. http://www.scrp.org/journal/ojs http://dx.do.org/0.436/ojs.05.5708 Stochastc Restrcted Maxmum Lkelhood Estmator n Logstc Regresson
More informationOn Graphs with Same Distance Distribution
Appled Mathematcs, 07, 8, 799-807 http://wwwscrporg/journal/am ISSN Onlne: 5-7393 ISSN Prnt: 5-7385 On Graphs wth Same Dstance Dstrbuton Xulang Qu, Xaofeng Guo,3 Chengy Unversty College, Jme Unversty,
More informationLiu-type Negative Binomial Regression: A Comparison of Recent Estimators and Applications
Lu-type Negatve Bnomal Regresson: A Comparson of Recent Estmators and Applcatons Yasn Asar Department of Mathematcs-Computer Scences, Necmettn Erbaan Unversty, Konya 4090, Turey, yasar@onya.edu.tr, yasnasar@hotmal.com
More informationRobust Logistic Ridge Regression Estimator in the Presence of High Leverage Multicollinear Observations
Mathematcal and Computatonal Methods n Scence and Engneerng Robust Logstc Rdge Regresson Estmator n the Presence of Hgh Leverage Multcollnear Observatons SYAIBA BALQISH ARIFFIN 1 AND HABSHAH MIDI 1, Faculty
More informationSOME NEW ADJUSTED RIDGE ESTIMATORS OF LINEAR REGRESSION MODEL
Internatonal Journal of Cvl Engneerng and Technology (IJCIET) Volume 9, Issue 11, November 18, pp. 838 85, Artcle ID: IJCIET_9_11_84 Avalable onlne at http://www.aeme.com/jcet/ssues.asp?jtype=ijciet&vtype=9&itype=11
More informationComparison of the Population Variance Estimators. of 2-Parameter Exponential Distribution Based on. Multiple Criteria Decision Making Method
Appled Mathematcal Scences, Vol. 7, 0, no. 47, 07-0 HIARI Ltd, www.m-hkar.com Comparson of the Populaton Varance Estmators of -Parameter Exponental Dstrbuton Based on Multple Crtera Decson Makng Method
More informationEcon107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4)
I. Classcal Assumptons Econ7 Appled Econometrcs Topc 3: Classcal Model (Studenmund, Chapter 4) We have defned OLS and studed some algebrac propertes of OLS. In ths topc we wll study statstcal propertes
More informationRidge Regression Estimators with the Problem. of Multicollinearity
Appled Mathematcal Scences, Vol. 7, 2013, no. 50, 2469-2480 HIKARI Ltd, www.m-hkar.com Rdge Regresson Estmators wth the Problem of Multcollnearty Mae M. Kamel Statstc Department, Faculty of Commerce Tanta
More informationRidge Estimator in Logistic Regression under Stochastic Linear Restrictions
British Journal of Mathematics & Computer Science 15(3): 1-14, 2016, Article no.bjmcs.24585 ISSN: 2231-0851 SCIENCEDOMAIN international www.sciencedomain.org Ridge Estimator in Logistic Regression under
More informationLINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity
LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 30 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 2 Remedes for multcollnearty Varous technques have
More informationLINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity
LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 31 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 6. Rdge regresson The OLSE s the best lnear unbased
More information[ ] λ λ λ. Multicollinearity. multicollinearity Ragnar Frisch (1934) perfect exact. collinearity. multicollinearity. exact
Multcollnearty multcollnearty Ragnar Frsch (934 perfect exact collnearty multcollnearty K exact λ λ λ K K x+ x+ + x 0 0.. λ, λ, λk 0 0.. x perfect ntercorrelated λ λ λ x+ x+ + KxK + v 0 0.. v 3 y β + β
More informationDERIVATION OF THE PROBABILITY PLOT CORRELATION COEFFICIENT TEST STATISTICS FOR THE GENERALIZED LOGISTIC DISTRIBUTION
Internatonal Worshop ADVANCES IN STATISTICAL HYDROLOGY May 3-5, Taormna, Italy DERIVATION OF THE PROBABILITY PLOT CORRELATION COEFFICIENT TEST STATISTICS FOR THE GENERALIZED LOGISTIC DISTRIBUTION by Sooyoung
More informationSimulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests
Smulated of the Cramér-von Mses Goodness-of-Ft Tests Steele, M., Chaselng, J. and 3 Hurst, C. School of Mathematcal and Physcal Scences, James Cook Unversty, Australan School of Envronmental Studes, Grffth
More informationNon-Mixture Cure Model for Interval Censored Data: Simulation Study ABSTRACT
Malaysan Journal of Mathematcal Scences 8(S): 37-44 (2014) Specal Issue: Internatonal Conference on Mathematcal Scences and Statstcs 2013 (ICMSS2013) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES Journal
More informationMaximum Likelihood Estimation of Binary Dependent Variables Models: Probit and Logit. 1. General Formulation of Binary Dependent Variables Models
ECO 452 -- OE 4: Probt and Logt Models ECO 452 -- OE 4 Maxmum Lkelhood Estmaton of Bnary Dependent Varables Models: Probt and Logt hs note demonstrates how to formulate bnary dependent varables models
More informationANOMALIES OF THE MAGNITUDE OF THE BIAS OF THE MAXIMUM LIKELIHOOD ESTIMATOR OF THE REGRESSION SLOPE
P a g e ANOMALIES OF THE MAGNITUDE OF THE BIAS OF THE MAXIMUM LIKELIHOOD ESTIMATOR OF THE REGRESSION SLOPE Darmud O Drscoll ¹, Donald E. Ramrez ² ¹ Head of Department of Mathematcs and Computer Studes
More informationThe Multiple Classical Linear Regression Model (CLRM): Specification and Assumptions. 1. Introduction
ECONOMICS 5* -- NOTE (Summary) ECON 5* -- NOTE The Multple Classcal Lnear Regresson Model (CLRM): Specfcaton and Assumptons. Introducton CLRM stands for the Classcal Lnear Regresson Model. The CLRM s also
More informationComputation of Higher Order Moments from Two Multinomial Overdispersion Likelihood Models
Computaton of Hgher Order Moments from Two Multnomal Overdsperson Lkelhood Models BY J. T. NEWCOMER, N. K. NEERCHAL Department of Mathematcs and Statstcs, Unversty of Maryland, Baltmore County, Baltmore,
More informationDurban Watson for Testing the Lack-of-Fit of Polynomial Regression Models without Replications
Durban Watson for Testng the Lack-of-Ft of Polynomal Regresson Models wthout Replcatons Ruba A. Alyaf, Maha A. Omar, Abdullah A. Al-Shha ralyaf@ksu.edu.sa, maomar@ksu.edu.sa, aalshha@ksu.edu.sa Department
More informationImproved Landweber Algorithm Based on Correlation
Journal of Modern Physcs, 07, 8, 547-556 http://www.scrp.org/ournal/mp ISSN Onlne: 53-0X ISSN Prnt: 53-96 Improved Landweber Algorthm Based on Correlaton Yqun Kang *, Sh Lu School of Control and Computer
More informationStatistics for Business and Economics
Statstcs for Busness and Economcs Chapter 11 Smple Regresson Copyrght 010 Pearson Educaton, Inc. Publshng as Prentce Hall Ch. 11-1 11.1 Overvew of Lnear Models n An equaton can be ft to show the best lnear
More informationAssociation for the Chi-square Test
Assocaton for the Ch-square Test Davd J Olve Southern Illnos Unversty February 8, 2012 Abstract A problem wth measures of assocaton for the ch-square test s that the measures depend on the number of observatons
More informationCOMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
More informationA Comparative Study for Estimation Parameters in Panel Data Model
A Comparatve Study for Estmaton Parameters n Panel Data Model Ahmed H. Youssef and Mohamed R. Abonazel hs paper examnes the panel data models when the regresson coeffcents are fxed random and mxed and
More informationA new Approach for Solving Linear Ordinary Differential Equations
, ISSN 974-57X (Onlne), ISSN 974-5718 (Prnt), Vol. ; Issue No. 1; Year 14, Copyrght 13-14 by CESER PUBLICATIONS A new Approach for Solvng Lnear Ordnary Dfferental Equatons Fawz Abdelwahd Department of
More informationOn Liu Estimators for the Logit Regression Model
CESIS Electronc Workng Paper Seres Paper No. 59 On Lu Estmators for the Logt Regresson Moel Krstofer Månsson B. M. Golam Kbra October 011 The Royal Insttute of technology Centre of Excellence for Scence
More informationOn Comparison of Some Ridge Parameters in Ridge Regression
Sr Lankan Journal of Aled Statstcs, Vol (15-1) On Comarson of Some Rdge Parameters n Rdge Regresson Ashok V. Dorugade Y C Mahavdyalaya Halkarn, Tal-Chandgad, Kolhaur, Maharashtra, Inda Corresondng Author:
More informationDO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR. Introductory Econometrics 1 hour 30 minutes
25/6 Canddates Only January Examnatons 26 Student Number: Desk Number:...... DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR Department Module Code Module Ttle Exam Duraton
More informationTest for Intraclass Correlation Coefficient under Unequal Family Sizes
Journal of Modern Appled Statstcal Methods Volume Issue Artcle 9 --03 Test for Intraclass Correlaton Coeffcent under Unequal Famly Szes Madhusudan Bhandary Columbus State Unversty, Columbus, GA, bhandary_madhusudan@colstate.edu
More informationExponential Type Product Estimator for Finite Population Mean with Information on Auxiliary Attribute
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 193-9466 Vol. 10, Issue 1 (June 015), pp. 106-113 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) Exponental Tpe Product Estmator
More informationNew Liu Estimators for the Poisson Regression Model: Method and Application
New Lu Estmators for the Posson Regresson Moel: Metho an Applcaton By Krstofer Månsson B. M. Golam Kbra, Pär Sölaner an Ghaz Shukur,3 Department of Economcs, Fnance an Statstcs, Jönköpng Unversty Jönköpng,
More informationEfficient nonresponse weighting adjustment using estimated response probability
Effcent nonresponse weghtng adjustment usng estmated response probablty Jae Kwang Km Department of Appled Statstcs, Yonse Unversty, Seoul, 120-749, KOREA Key Words: Regresson estmator, Propensty score,
More informationImprovement in Estimating the Population Mean Using Exponential Estimator in Simple Random Sampling
Bulletn of Statstcs & Economcs Autumn 009; Volume 3; Number A09; Bull. Stat. Econ. ISSN 0973-70; Copyrght 009 by BSE CESER Improvement n Estmatng the Populaton Mean Usng Eponental Estmator n Smple Random
More informationSome Robust Ridge Regression for handling Multicollinearity and Outlier
Internatonal Journal of Scences: Basc and Appled Research (IJSBAR) ISSN 307-4531 (Prnt & Onlne) http://gssrr.org/ndex.php?journal=journalofbascandappled ----------------------------------------------------------------------------------------------------------------
More informationEstimation: Part 2. Chapter GREG estimation
Chapter 9 Estmaton: Part 2 9. GREG estmaton In Chapter 8, we have seen that the regresson estmator s an effcent estmator when there s a lnear relatonshp between y and x. In ths chapter, we generalzed the
More informationDepartment of Quantitative Methods & Information Systems. Time Series and Their Components QMIS 320. Chapter 6
Department of Quanttatve Methods & Informaton Systems Tme Seres and Ther Components QMIS 30 Chapter 6 Fall 00 Dr. Mohammad Zanal These sldes were modfed from ther orgnal source for educatonal purpose only.
More informationDiscussion of Extensions of the Gauss-Markov Theorem to the Case of Stochastic Regression Coefficients Ed Stanek
Dscusson of Extensons of the Gauss-arkov Theorem to the Case of Stochastc Regresson Coeffcents Ed Stanek Introducton Pfeffermann (984 dscusses extensons to the Gauss-arkov Theorem n settngs where regresson
More informationOn an Extension of Stochastic Approximation EM Algorithm for Incomplete Data Problems. Vahid Tadayon 1
On an Extenson of Stochastc Approxmaton EM Algorthm for Incomplete Data Problems Vahd Tadayon Abstract: The Stochastc Approxmaton EM (SAEM algorthm, a varant stochastc approxmaton of EM, s a versatle tool
More informationA Note on Test of Homogeneity Against Umbrella Scale Alternative Based on U-Statistics
J Stat Appl Pro No 3 93- () 93 NSP Journal of Statstcs Applcatons & Probablty --- An Internatonal Journal @ NSP Natural Scences Publshng Cor A Note on Test of Homogenety Aganst Umbrella Scale Alternatve
More informationResearch Article Green s Theorem for Sign Data
Internatonal Scholarly Research Network ISRN Appled Mathematcs Volume 2012, Artcle ID 539359, 10 pages do:10.5402/2012/539359 Research Artcle Green s Theorem for Sgn Data Lous M. Houston The Unversty of
More informationThe Order Relation and Trace Inequalities for. Hermitian Operators
Internatonal Mathematcal Forum, Vol 3, 08, no, 507-57 HIKARI Ltd, wwwm-hkarcom https://doorg/0988/mf088055 The Order Relaton and Trace Inequaltes for Hermtan Operators Y Huang School of Informaton Scence
More informationInternational Journal of Engineering Research and Modern Education (IJERME) Impact Factor: 7.018, ISSN (Online): (
CONSTRUCTION AND SELECTION OF CHAIN SAMPLING PLAN WITH ZERO INFLATED POISSON DISTRIBUTION A. Palansamy* & M. Latha** * Research Scholar, Department of Statstcs, Government Arts College, Udumalpet, Tamlnadu
More informationSee Book Chapter 11 2 nd Edition (Chapter 10 1 st Edition)
Count Data Models See Book Chapter 11 2 nd Edton (Chapter 10 1 st Edton) Count data consst of non-negatve nteger values Examples: number of drver route changes per week, the number of trp departure changes
More informationA note on regression estimation with unknown population size
Statstcs Publcatons Statstcs 6-016 A note on regresson estmaton wth unknown populaton sze Mchael A. Hdroglou Statstcs Canada Jae Kwang Km Iowa State Unversty jkm@astate.edu Chrstan Olver Nambeu Statstcs
More informationTesting for outliers in nonlinear longitudinal data models based on M-estimation
ISS 1746-7659, England, UK Journal of Informaton and Computng Scence Vol 1, o, 017, pp107-11 estng for outlers n nonlnear longtudnal data models based on M-estmaton Huhu Sun 1 1 School of Mathematcs and
More informationMaximum Likelihood Estimation of Binary Dependent Variables Models: Probit and Logit. 1. General Formulation of Binary Dependent Variables Models
ECO 452 -- OE 4: Probt and Logt Models ECO 452 -- OE 4 Mamum Lkelhood Estmaton of Bnary Dependent Varables Models: Probt and Logt hs note demonstrates how to formulate bnary dependent varables models for
More informationStatistical inference for generalized Pareto distribution based on progressive Type-II censored data with random removals
Internatonal Journal of Scentfc World, 2 1) 2014) 1-9 c Scence Publshng Corporaton www.scencepubco.com/ndex.php/ijsw do: 10.14419/jsw.v21.1780 Research Paper Statstcal nference for generalzed Pareto dstrbuton
More informationLECTURE 9 CANONICAL CORRELATION ANALYSIS
LECURE 9 CANONICAL CORRELAION ANALYSIS Introducton he concept of canoncal correlaton arses when we want to quantfy the assocatons between two sets of varables. For example, suppose that the frst set of
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Exerments-I MODULE III LECTURE - 2 EXPERIMENTAL DESIGN MODELS Dr. Shalabh Deartment of Mathematcs and Statstcs Indan Insttute of Technology Kanur 2 We consder the models
More informationInterval Estimation of Stress-Strength Reliability for a General Exponential Form Distribution with Different Unknown Parameters
Internatonal Journal of Statstcs and Probablty; Vol. 6, No. 6; November 17 ISSN 197-73 E-ISSN 197-74 Publshed by Canadan Center of Scence and Educaton Interval Estmaton of Stress-Strength Relablty for
More informationPredictive Analytics : QM901.1x Prof U Dinesh Kumar, IIMB. All Rights Reserved, Indian Institute of Management Bangalore
Sesson Outlne Introducton to classfcaton problems and dscrete choce models. Introducton to Logstcs Regresson. Logstc functon and Logt functon. Maxmum Lkelhood Estmator (MLE) for estmaton of LR parameters.
More informationUsing Multivariate Rank Sum Tests to Evaluate Effectiveness of Computer Applications in Teaching Business Statistics
Usng Multvarate Rank Sum Tests to Evaluate Effectveness of Computer Applcatons n Teachng Busness Statstcs by Yeong-Tzay Su, Professor Department of Mathematcs Kaohsung Normal Unversty Kaohsung, TAIWAN
More informationUsing T.O.M to Estimate Parameter of distributions that have not Single Exponential Family
IOSR Journal of Mathematcs IOSR-JM) ISSN: 2278-5728. Volume 3, Issue 3 Sep-Oct. 202), PP 44-48 www.osrjournals.org Usng T.O.M to Estmate Parameter of dstrbutons that have not Sngle Exponental Famly Jubran
More informationLinear Approximation with Regularization and Moving Least Squares
Lnear Approxmaton wth Regularzaton and Movng Least Squares Igor Grešovn May 007 Revson 4.6 (Revson : March 004). 5 4 3 0.5 3 3.5 4 Contents: Lnear Fttng...4. Weghted Least Squares n Functon Approxmaton...
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Experment-I MODULE VII LECTURE - 3 ANALYSIS OF COVARIANCE Dr Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Any scentfc experment s performed
More informationStatistics for Managers Using Microsoft Excel/SPSS Chapter 13 The Simple Linear Regression Model and Correlation
Statstcs for Managers Usng Mcrosoft Excel/SPSS Chapter 13 The Smple Lnear Regresson Model and Correlaton 1999 Prentce-Hall, Inc. Chap. 13-1 Chapter Topcs Types of Regresson Models Determnng the Smple Lnear
More informationTesting for seasonal unit roots in heterogeneous panels
Testng for seasonal unt roots n heterogeneous panels Jesus Otero * Facultad de Economía Unversdad del Rosaro, Colomba Jeremy Smth Department of Economcs Unversty of arwck Monca Gulett Aston Busness School
More informationOn Outlier Robust Small Area Mean Estimate Based on Prediction of Empirical Distribution Function
On Outler Robust Small Area Mean Estmate Based on Predcton of Emprcal Dstrbuton Functon Payam Mokhtaran Natonal Insttute of Appled Statstcs Research Australa Unversty of Wollongong Small Area Estmaton
More informationAndreas C. Drichoutis Agriculural University of Athens. Abstract
Heteroskedastcty, the sngle crossng property and ordered response models Andreas C. Drchouts Agrculural Unversty of Athens Panagots Lazards Agrculural Unversty of Athens Rodolfo M. Nayga, Jr. Texas AMUnversty
More informationx i1 =1 for all i (the constant ).
Chapter 5 The Multple Regresson Model Consder an economc model where the dependent varable s a functon of K explanatory varables. The economc model has the form: y = f ( x,x,..., ) xk Approxmate ths by
More informationRegularized Discriminant Analysis for Face Recognition
1 Regularzed Dscrmnant Analyss for Face Recognton Itz Pma, Mayer Aladem Department of Electrcal and Computer Engneerng, Ben-Guron Unversty of the Negev P.O.Box 653, Beer-Sheva, 845, Israel. Abstract Ths
More informationEconometrics of Panel Data
Econometrcs of Panel Data Jakub Mućk Meetng # 8 Jakub Mućk Econometrcs of Panel Data Meetng # 8 1 / 17 Outlne 1 Heterogenety n the slope coeffcents 2 Seemngly Unrelated Regresson (SUR) 3 Swamy s random
More informationA Monte Carlo Study for Swamy s Estimate of Random Coefficient Panel Data Model
A Monte Carlo Study for Swamy s Estmate of Random Coeffcent Panel Data Model Aman Mousa, Ahmed H. Youssef and Mohamed R. Abonazel Department of Appled Statstcs and Econometrcs, Instute of Statstcal Studes
More informationChapter 15 - Multiple Regression
Chapter - Multple Regresson Chapter - Multple Regresson Multple Regresson Model The equaton that descrbes how the dependent varable y s related to the ndependent varables x, x,... x p and an error term
More informationLOW BIAS INTEGRATED PATH ESTIMATORS. James M. Calvin
Proceedngs of the 007 Wnter Smulaton Conference S G Henderson, B Bller, M-H Hseh, J Shortle, J D Tew, and R R Barton, eds LOW BIAS INTEGRATED PATH ESTIMATORS James M Calvn Department of Computer Scence
More informationImproved Approximation Methods to the Stopped Sum Distribution
Internatonal Journal of Mathematcal Analyss and Applcatons 2017; 4(6): 42-46 http://www.aasct.org/journal/jmaa ISSN: 2375-3927 Improved Approxmaton Methods to the Stopped Sum Dstrbuton Aman Al Rashd *,
More informationChapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems
Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons
More informationChapter 11: Simple Linear Regression and Correlation
Chapter 11: Smple Lnear Regresson and Correlaton 11-1 Emprcal Models 11-2 Smple Lnear Regresson 11-3 Propertes of the Least Squares Estmators 11-4 Hypothess Test n Smple Lnear Regresson 11-4.1 Use of t-tests
More informationStatistics for Economics & Business
Statstcs for Economcs & Busness Smple Lnear Regresson Learnng Objectves In ths chapter, you learn: How to use regresson analyss to predct the value of a dependent varable based on an ndependent varable
More informationThis column is a continuation of our previous column
Comparson of Goodness of Ft Statstcs for Lnear Regresson, Part II The authors contnue ther dscusson of the correlaton coeffcent n developng a calbraton for quanttatve analyss. Jerome Workman Jr. and Howard
More informationComparison among Some Remedial Procedures for Solving. Multicollinearity Problem in Regression Model Using Simulation. Ashraf Noureddin Dawod Ababneh
Comparson among Some Remedal Procedures for Solvng Multcollnearty Problem n Regresson Model Usng Smulaton By Ashraf Noureddn Dawod Ababneh Supervsor Prof.Fars M. Al-Athar hs hess was submtted n Partal
More informationDETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM
Ganj, Z. Z., et al.: Determnaton of Temperature Dstrbuton for S111 DETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM by Davood Domr GANJI
More informationANSWERS. Problem 1. and the moment generating function (mgf) by. defined for any real t. Use this to show that E( U) var( U)
Econ 413 Exam 13 H ANSWERS Settet er nndelt 9 deloppgaver, A,B,C, som alle anbefales å telle lkt for å gøre det ltt lettere å stå. Svar er gtt . Unfortunately, there s a prntng error n the hnt of
More informationUSE OF DOUBLE SAMPLING SCHEME IN ESTIMATING THE MEAN OF STRATIFIED POPULATION UNDER NON-RESPONSE
STATISTICA, anno LXXV, n. 4, 015 USE OF DOUBLE SAMPLING SCHEME IN ESTIMATING THE MEAN OF STRATIFIED POPULATION UNDER NON-RESPONSE Manoj K. Chaudhary 1 Department of Statstcs, Banaras Hndu Unversty, Varanas,
More informationAsymptotics of the Solution of a Boundary Value. Problem for One-Characteristic Differential. Equation Degenerating into a Parabolic Equation
Nonl. Analyss and Dfferental Equatons, ol., 4, no., 5 - HIKARI Ltd, www.m-har.com http://dx.do.org/.988/nade.4.456 Asymptotcs of the Soluton of a Boundary alue Problem for One-Characterstc Dfferental Equaton
More informationBayesian predictive Configural Frequency Analysis
Psychologcal Test and Assessment Modelng, Volume 54, 2012 (3), 285-292 Bayesan predctve Confgural Frequency Analyss Eduardo Gutérrez-Peña 1 Abstract Confgural Frequency Analyss s a method for cell-wse
More informationASYMPTOTIC PROPERTIES OF ESTIMATES FOR THE PARAMETERS IN THE LOGISTIC REGRESSION MODEL
Asymptotc Asan-Afrcan Propertes Journal of Estmates Economcs for and the Econometrcs, Parameters n Vol. the Logstc, No., Regresson 20: 65-74 Model 65 ASYMPTOTIC PROPERTIES OF ESTIMATES FOR THE PARAMETERS
More informationLow default modelling: a comparison of techniques based on a real Brazilian corporate portfolio
Low default modellng: a comparson of technques based on a real Brazlan corporate portfolo MSc Gulherme Fernandes and MSc Carlos Rocha Credt Scorng and Credt Control Conference XII August 2011 Analytcs
More informationPolynomial Regression Models
LINEAR REGRESSION ANALYSIS MODULE XII Lecture - 6 Polynomal Regresson Models Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Test of sgnfcance To test the sgnfcance
More informationOn mutual information estimation for mixed-pair random variables
On mutual nformaton estmaton for mxed-par random varables November 3, 218 Aleksandr Beknazaryan, Xn Dang and Haln Sang 1 Department of Mathematcs, The Unversty of Msssspp, Unversty, MS 38677, USA. E-mal:
More informationChapter 13: Multiple Regression
Chapter 13: Multple Regresson 13.1 Developng the multple-regresson Model The general model can be descrbed as: It smplfes for two ndependent varables: The sample ft parameter b 0, b 1, and b are used to
More informationThe binomial transforms of the generalized (s, t )-Jacobsthal matrix sequence
Int. J. Adv. Appl. Math. and Mech. 6(3 (2019 14 20 (ISSN: 2347-2529 Journal homepage: www.jaamm.com IJAAMM Internatonal Journal of Advances n Appled Mathematcs and Mechancs The bnomal transforms of the
More informationDouble Acceptance Sampling Plan for Time Truncated Life Tests Based on Transmuted Generalized Inverse Weibull Distribution
J. Stat. Appl. Pro. 6, No. 1, 1-6 2017 1 Journal of Statstcs Applcatons & Probablty An Internatonal Journal http://dx.do.org/10.18576/jsap/060101 Double Acceptance Samplng Plan for Tme Truncated Lfe Tests
More informationA Robust Method for Calculating the Correlation Coefficient
A Robust Method for Calculatng the Correlaton Coeffcent E.B. Nven and C. V. Deutsch Relatonshps between prmary and secondary data are frequently quantfed usng the correlaton coeffcent; however, the tradtonal
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Experment-I MODULE VIII LECTURE - 34 ANALYSIS OF VARIANCE IN RANDOM-EFFECTS MODEL AND MIXED-EFFECTS EFFECTS MODEL Dr Shalabh Department of Mathematcs and Statstcs Indan
More informationLecture 9: Linear regression: centering, hypothesis testing, multiple covariates, and confounding
Recall: man dea of lnear regresson Lecture 9: Lnear regresson: centerng, hypothess testng, multple covarates, and confoundng Sandy Eckel seckel@jhsph.edu 6 May 8 Lnear regresson can be used to study an
More informationLecture 9: Linear regression: centering, hypothesis testing, multiple covariates, and confounding
Lecture 9: Lnear regresson: centerng, hypothess testng, multple covarates, and confoundng Sandy Eckel seckel@jhsph.edu 6 May 008 Recall: man dea of lnear regresson Lnear regresson can be used to study
More informationEcon Statistical Properties of the OLS estimator. Sanjaya DeSilva
Econ 39 - Statstcal Propertes of the OLS estmator Sanjaya DeSlva September, 008 1 Overvew Recall that the true regresson model s Y = β 0 + β 1 X + u (1) Applyng the OLS method to a sample of data, we estmate
More informationBayesian Planning of Hit-Miss Inspection Tests
Bayesan Plannng of Ht-Mss Inspecton Tests Yew-Meng Koh a and Wllam Q Meeker a a Center for Nondestructve Evaluaton, Department of Statstcs, Iowa State Unversty, Ames, Iowa 5000 Abstract Although some useful
More informationwhere I = (n x n) diagonal identity matrix with diagonal elements = 1 and off-diagonal elements = 0; and σ 2 e = variance of (Y X).
11.4.1 Estmaton of Multple Regresson Coeffcents In multple lnear regresson, we essentally solve n equatons for the p unnown parameters. hus n must e equal to or greater than p and n practce n should e
More informationAn (almost) unbiased estimator for the S-Gini index
An (almost unbased estmator for the S-Gn ndex Thomas Demuynck February 25, 2009 Abstract Ths note provdes an unbased estmator for the absolute S-Gn and an almost unbased estmator for the relatve S-Gn for
More informationComposite Hypotheses testing
Composte ypotheses testng In many hypothess testng problems there are many possble dstrbutons that can occur under each of the hypotheses. The output of the source s a set of parameters (ponts n a parameter
More informationHowever, since P is a symmetric idempotent matrix, of P are either 0 or 1 [Eigen-values
Fall 007 Soluton to Mdterm Examnaton STAT 7 Dr. Goel. [0 ponts] For the general lnear model = X + ε, wth uncorrelated errors havng mean zero and varance σ, suppose that the desgn matrx X s not necessarly
More informationThe Quadratic Trigonometric Bézier Curve with Single Shape Parameter
J. Basc. Appl. Sc. Res., (3541-546, 01 01, TextRoad Publcaton ISSN 090-4304 Journal of Basc and Appled Scentfc Research www.textroad.com The Quadratc Trgonometrc Bézer Curve wth Sngle Shape Parameter Uzma
More informationParametric fractional imputation for missing data analysis. Jae Kwang Kim Survey Working Group Seminar March 29, 2010
Parametrc fractonal mputaton for mssng data analyss Jae Kwang Km Survey Workng Group Semnar March 29, 2010 1 Outlne Introducton Proposed method Fractonal mputaton Approxmaton Varance estmaton Multple mputaton
More informationLecture 6: Introduction to Linear Regression
Lecture 6: Introducton to Lnear Regresson An Manchakul amancha@jhsph.edu 24 Aprl 27 Lnear regresson: man dea Lnear regresson can be used to study an outcome as a lnear functon of a predctor Example: 6
More informationChapter 9: Statistical Inference and the Relationship between Two Variables
Chapter 9: Statstcal Inference and the Relatonshp between Two Varables Key Words The Regresson Model The Sample Regresson Equaton The Pearson Correlaton Coeffcent Learnng Outcomes After studyng ths chapter,
More informationNegative Binomial Regression
STATGRAPHICS Rev. 9/16/2013 Negatve Bnomal Regresson Summary... 1 Data Input... 3 Statstcal Model... 3 Analyss Summary... 4 Analyss Optons... 7 Plot of Ftted Model... 8 Observed Versus Predcted... 10 Predctons...
More informationImproved Class of Ratio Estimators for Finite Population Variance
Global Journal of Scence Fronter Research: F Mathematcs and Decson Scences Volume 6 Issue Verson.0 Year 06 Tpe : Double lnd Peer Revewed Internatonal Research Journal Publsher: Global Journals Inc. (USA)
More information