LEADER 05814nam 2200685 450 001 9910132350603321 005 20170810190648.0 010 $a1-118-85396-2 010 $a1-118-85392-X 010 $a1-118-85393-8 035 $a(CKB)3710000000251854 035 $a(EBL)1810511 035 $a(SSID)ssj0001348340 035 $a(PQKBManifestationID)11775629 035 $a(PQKBTitleCode)TC0001348340 035 $a(PQKBWorkID)11372227 035 $a(PQKB)11618509 035 $a(MiAaPQ)EBC1810511 035 $a(DLC) 2014011507 035 $a(CaSebORM)9781118853962 035 $a(PPN)192687441 035 $a(EXLCZ)993710000000251854 100 $a20141014h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStatistical inference for models with multivariate t-distributed errors /$fA. K. Md. Ehsanes Saleh, M. Arashi, S. M. M. Tabatabaey 205 $a1st edition 210 1$aHoboken, New Jersey :$cJohn Wiley & Sons,$d2014. 210 4$dİ2014 215 $a1 online resource (275 p.) 300 $aDescription based upon print version of record. 311 $a1-322-19613-3 311 $a1-118-85405-5 320 $aIncludes bibliographical references and indexes. 327 $aCover; Title Page; Copyright Page; CONTENTS; List of Figures; List of Tables; Preface; Glossary; List of Symbols; 1 Introduction; 1.1 Objective of the Book; 1.2 Models under Consideration; 1.2.1 Location Model; 1.2.2 Simple Linear Model; 1.2.3 ANOVA Model; 1.2.4 Parallelism Model; 1.2.5 Multiple Regression Model; 1.2.6 Ridge Regression; 1.2.7 Multivariate Model; 1.2.8 Simple Multivariate Linear Model; 1.3 Organization of the Book; 1.4 Problems; 2 Preliminaries; 2.1 Normal Distribution; 2.2 Chi-Square Distribution; 2.3 Student''s t-Distribution; 2.4 F-Distribution 327 $a2.5 Multivariate Normal Distribution2.6 Multivariate t-Distribution; 2.6.1 Expected Values of Functions of M_t^(p)(? , ?^2V_p, ?o) - Variables; 2.6.2 Sampling Distribution of Quadratic Forms; 2.6.3 Distribution of Linear Functions of t-Variables; 2.7 Problems; 3 Location Model; 3.1 Model Specification; 3.2 Unbiased Estimates of ? and ?^2 and Test of Hypothesis; 3.3 Estimators; 3.4 Bias and MSE Expressions of the Location Estimators; 3.4.1 Analysis of the Estimators of Location Parameter; 3.5 Various Estimates of Variance; 3.5.1 Bias and MSE Expressions of the Variance Estimators 327 $a3.5.2 Analysis of the Estimators of the Variance Parameter3.6 Problems; 4 Simple Regression Model; 4.1 Introduction; 4.2 Estimation and Testing of ?; 4.2.1 Estimation of ?; 4.2.2 Test of Intercept Parameter; 4.2.3 Estimators of ? and ?; 4.3 Properties of Intercept Parameter; 4.3.1 Bias Expressions of the Estimators; 4.3.2 MSE Expressions of the Estimators; 4.4 Comparison; 4.4.1 Optimum Level of Significance of ?_n^PT; 4.5 Numerical Illustration; 4.6 Problems; 5 ANOVA; 5.1 Model Specification; 5.2 Proposed Estimators and Testing; 5.3 Bias, MSE, and Risk Expressions; 5.4 Risk Analysis 327 $a5.4.1 Comparison of ?_n and ?_n5.4.2 Comparison of ?_n_PT and ?_n(?_n); 5.4.3 Comparison of ?_n^S, ?_n , ?n, and ?_n^PT; 5.4.4 Comparison of ?_n^S and ?_n^S+; 5.5 Problems; 6 Parallelism Model; 6.1 Model Specification; 6.2 Estimation of the Parameters and Test of Parallelism; 6.2.1 Test of Parallelism; 6.3 Bias, MSE, and Risk Expressions; 6.3.1 Expressions of Bias, MSE Matrix, and Risks of ?_n, ?_n, ?_n, and ?_n; 6.3.2 Expressions of Bias, MSE Matrix, and Risks of the PTEs of ? and ?; 6.3.3 Expressions of Bias, MSE Matrix, and Risks of the SSEs of ? and ? 327 $a6.3.4 Expressions of Bias, MSE Matrix, and Risks of the PRSEs of ? and ?6.4 Risk Analysis; 6.5 Problems; 7 Multiple Regression Model; 7.1 Model Specification; 7.2 Shrinkage Estimators and Testing; 7.3 Bias and Risk Expressions; 7.3.1 Balanced Loss Function; 7.3.2 Properties; 7.4 Comparison; 7.5 Problems; 8 Ridge Regression; 8.1 Model Specification; 8.2 Proposed Estimators; 8.3 Bias, MSE, and Risk Expressions; 8.3.1 Biases of the Estimators; 8.3.2 MSE Matrices and Risks of the Estimators; 8.4 Performance of the Estimators; 8.4.1 Comparison between ?_n(k), ?_n^S(k), and ?_n^S+(k) 327 $a8.4.2 Comparison between ?_n (k) and ?_n^PT (k) 330 $a"This book summarizes the results of various models under normal theory with a brief review of the literature. Statistical Inference for Models with Multivariate t-Distributed Errors: Includes a wide array of applications for the analysis of multivariate observations Emphasizes the development of linear statistical models with applications to engineering, the physical sciences, and mathematics Contains an up-to-date bibliography featuring the latest trends and advances in the field to provide a collective source for research on the topic Addresses linear regression models with non-normal errors with practical real-world examples Uniquely addresses regression models in Student's t-distributed errors and t-models Supplemented with an Instructor's Solutions Manual, which is available via written request by the Publisher "--$cProvided by publisher. 606 $aRegression analysis 606 $aMultivariate analysis 615 0$aRegression analysis. 615 0$aMultivariate analysis. 676 $a519.536 686 $aMAT029030$aMAT029010$aMAT029020$2bisacsh 700 $aSaleh$b A. K. Md. Ehsanes$0150888 702 $aArashi$b M. 702 $aTabatabaey$b S. M. M. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910132350603321 996 $aStatistical inference for models with multivariate t-distributed errors$91984568 997 $aUNINA