A. K. Md. Ehsanes Saleh, Mohammad Arashi, S. M. M. Tabatabaey
Statistical Inference for Models with Multivariate t-Distributed Errors
A. K. Md. Ehsanes Saleh, Mohammad Arashi, S. M. M. Tabatabaey
Statistical Inference for Models with Multivariate t-Distributed Errors
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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…mehr
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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
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
Produktdetails
- Produktdetails
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 272
- Erscheinungstermin: 15. September 2014
- Englisch
- Abmessung: 236mm x 157mm x 18mm
- Gewicht: 499g
- ISBN-13: 9781118854051
- ISBN-10: 1118854055
- Artikelnr.: 40054663
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 272
- Erscheinungstermin: 15. September 2014
- Englisch
- Abmessung: 236mm x 157mm x 18mm
- Gewicht: 499g
- ISBN-13: 9781118854051
- ISBN-10: 1118854055
- Artikelnr.: 40054663
A. K. Md. Ehsanes Saleh, PhD, is Professor Emeritus and Distinguished Research Professor in the School of Mathematics and Statistics at Carleton University, Canada. He has published well-over 200 journal articles, and his research interests include nonparametric statistics, order statistics, and robust estimation. Dr. Saleh is a Fellow of the Institute of Mathematical Statistics, the American Statistical Association, and the Bangladesh Academy of Sciences. M. Arashi, PhD, is Associate Professor in the Department of Statistics at Shahrood University of Technology, Iran. The recipient of the Award for Teaching Excellence from Shahrood University in 2013, his research interests include shrinkage estimation, distribution theory, and multivariate analysis. S. M. M. Tabatabaey, PhD, is Associate Professor in the Department of Statistics at Ferdowski University of Mashhad, Iran. The author of over fifteen journal articles, he is also a member of the Institute of Mathematical Statistics and the Iranian Statistical Society.
List of Figures xv List of Tables xvii Preface xix Glossary xxi List of
Symbols xxiii 1 Introduction 1 1.1 Objective of the Book 1 1.2 Models Under
Consideration 3 2 Preliminaries 7 2.1 Normal distribution 8 2.2 Chisquare
distribution 8 2.3 Student's t distributions 10 2.4 F distribution 14 2.5
Multivariate Normal distribution 16 2.6 Multivariate t distribution 17 2.7
Problems 28 3 Location Model 31 3.1 Model Specification 32 3.2 Unbiased
Estimates of _ and _² and test of hypothesis 32 3.3 Estimators 36 3.4 Bias
and MSE Expressions of the Location Estimators 38 3.5 Various Estimates of
Variance 48 3.6 Problems 60 4 Simple Regression Model 61 4.1 Introduction
62 4.2 Estimation and Testing of _ 62 4.3 Properties of Intercept Parameter
66 4.4 Comparison 69 4.5 Numerical Illustration 72 4.6 Problems 77 5 ANOVA
79 5.1 Model Specification 80 5.2 Proposed Estimators and Testing 80 5.3
Bias, MSE and Risk Expressions 85 5.4 Risk Analysis 87 5.5 Problems 93 6
Parallelism Model 95 6.1 Model Specification 96 6.2 Estimation of the
Parameters and Test of Parallelism 97 6.3 Bias, MSE, and Risk Expressions
103 6.4 Risk Analysis 106 6.5 Problems 110 7 Multiple Regression Model 111
7.1 Model Specification 112 7.2 Shrinkage Estimators and Testing 112 7.3
Bias and Risk Expressions 116 7.4 Comparison 120 7.5 Problems 126 8 Ridge
Regression 127 8.1 Model Specification 128 8.2 Proposed Estimators 129 8.3
Bias, MSE, and Risk Expressions 130 8.4 Performance of the Estimators 135
8.5 Choice of Ridge Parameter 153 8.6 Problems 164 9 Multivariate Models
165 9.1 Location Model 166 9.2 Testing of Hypothesis and Several Estimators
of Local Parameter 167 9.3 Bias, Quadratic Bias, MSE, and Risk Expressions
169 9.4 Risk Analysis of the Estimators 171 9.5 Simple Multivariate Linear
Model 175 9.6 Problems 180 10 Bayesian Analysis 181 10.1 Introduction
(Zellner's Model) 181 10.2 Conditional Bayesian Inference 183 10.3 Matrix
Variate t Distribution 185 10.4 Bayesian Analysis in Multivariate
Regression Model 187 10.5 Problems 194 11 Linear Prediction Models 195 11.1
Model & Preliminaries 196 11.2 Distribution of SRV and RSS 197 11.3
Regression Model for Future Responses 199 11.4 Predictive Distributions of
FRV and FRSS 200 11.5 An Illustration 206 11.6 Problems 208 12 Stein
Estimation 209 12.1 Class of Estimators 210 12.2 Preliminaries and Some
Theorems 213 12.3 Superiority Conditions 216 12.4 Problems 223 References
225 Subject Index 243
Symbols xxiii 1 Introduction 1 1.1 Objective of the Book 1 1.2 Models Under
Consideration 3 2 Preliminaries 7 2.1 Normal distribution 8 2.2 Chisquare
distribution 8 2.3 Student's t distributions 10 2.4 F distribution 14 2.5
Multivariate Normal distribution 16 2.6 Multivariate t distribution 17 2.7
Problems 28 3 Location Model 31 3.1 Model Specification 32 3.2 Unbiased
Estimates of _ and _² and test of hypothesis 32 3.3 Estimators 36 3.4 Bias
and MSE Expressions of the Location Estimators 38 3.5 Various Estimates of
Variance 48 3.6 Problems 60 4 Simple Regression Model 61 4.1 Introduction
62 4.2 Estimation and Testing of _ 62 4.3 Properties of Intercept Parameter
66 4.4 Comparison 69 4.5 Numerical Illustration 72 4.6 Problems 77 5 ANOVA
79 5.1 Model Specification 80 5.2 Proposed Estimators and Testing 80 5.3
Bias, MSE and Risk Expressions 85 5.4 Risk Analysis 87 5.5 Problems 93 6
Parallelism Model 95 6.1 Model Specification 96 6.2 Estimation of the
Parameters and Test of Parallelism 97 6.3 Bias, MSE, and Risk Expressions
103 6.4 Risk Analysis 106 6.5 Problems 110 7 Multiple Regression Model 111
7.1 Model Specification 112 7.2 Shrinkage Estimators and Testing 112 7.3
Bias and Risk Expressions 116 7.4 Comparison 120 7.5 Problems 126 8 Ridge
Regression 127 8.1 Model Specification 128 8.2 Proposed Estimators 129 8.3
Bias, MSE, and Risk Expressions 130 8.4 Performance of the Estimators 135
8.5 Choice of Ridge Parameter 153 8.6 Problems 164 9 Multivariate Models
165 9.1 Location Model 166 9.2 Testing of Hypothesis and Several Estimators
of Local Parameter 167 9.3 Bias, Quadratic Bias, MSE, and Risk Expressions
169 9.4 Risk Analysis of the Estimators 171 9.5 Simple Multivariate Linear
Model 175 9.6 Problems 180 10 Bayesian Analysis 181 10.1 Introduction
(Zellner's Model) 181 10.2 Conditional Bayesian Inference 183 10.3 Matrix
Variate t Distribution 185 10.4 Bayesian Analysis in Multivariate
Regression Model 187 10.5 Problems 194 11 Linear Prediction Models 195 11.1
Model & Preliminaries 196 11.2 Distribution of SRV and RSS 197 11.3
Regression Model for Future Responses 199 11.4 Predictive Distributions of
FRV and FRSS 200 11.5 An Illustration 206 11.6 Problems 208 12 Stein
Estimation 209 12.1 Class of Estimators 210 12.2 Preliminaries and Some
Theorems 213 12.3 Superiority Conditions 216 12.4 Problems 223 References
225 Subject Index 243
List of Figures xv List of Tables xvii Preface xix Glossary xxi List of
Symbols xxiii 1 Introduction 1 1.1 Objective of the Book 1 1.2 Models Under
Consideration 3 2 Preliminaries 7 2.1 Normal distribution 8 2.2 Chisquare
distribution 8 2.3 Student's t distributions 10 2.4 F distribution 14 2.5
Multivariate Normal distribution 16 2.6 Multivariate t distribution 17 2.7
Problems 28 3 Location Model 31 3.1 Model Specification 32 3.2 Unbiased
Estimates of _ and _² and test of hypothesis 32 3.3 Estimators 36 3.4 Bias
and MSE Expressions of the Location Estimators 38 3.5 Various Estimates of
Variance 48 3.6 Problems 60 4 Simple Regression Model 61 4.1 Introduction
62 4.2 Estimation and Testing of _ 62 4.3 Properties of Intercept Parameter
66 4.4 Comparison 69 4.5 Numerical Illustration 72 4.6 Problems 77 5 ANOVA
79 5.1 Model Specification 80 5.2 Proposed Estimators and Testing 80 5.3
Bias, MSE and Risk Expressions 85 5.4 Risk Analysis 87 5.5 Problems 93 6
Parallelism Model 95 6.1 Model Specification 96 6.2 Estimation of the
Parameters and Test of Parallelism 97 6.3 Bias, MSE, and Risk Expressions
103 6.4 Risk Analysis 106 6.5 Problems 110 7 Multiple Regression Model 111
7.1 Model Specification 112 7.2 Shrinkage Estimators and Testing 112 7.3
Bias and Risk Expressions 116 7.4 Comparison 120 7.5 Problems 126 8 Ridge
Regression 127 8.1 Model Specification 128 8.2 Proposed Estimators 129 8.3
Bias, MSE, and Risk Expressions 130 8.4 Performance of the Estimators 135
8.5 Choice of Ridge Parameter 153 8.6 Problems 164 9 Multivariate Models
165 9.1 Location Model 166 9.2 Testing of Hypothesis and Several Estimators
of Local Parameter 167 9.3 Bias, Quadratic Bias, MSE, and Risk Expressions
169 9.4 Risk Analysis of the Estimators 171 9.5 Simple Multivariate Linear
Model 175 9.6 Problems 180 10 Bayesian Analysis 181 10.1 Introduction
(Zellner's Model) 181 10.2 Conditional Bayesian Inference 183 10.3 Matrix
Variate t Distribution 185 10.4 Bayesian Analysis in Multivariate
Regression Model 187 10.5 Problems 194 11 Linear Prediction Models 195 11.1
Model & Preliminaries 196 11.2 Distribution of SRV and RSS 197 11.3
Regression Model for Future Responses 199 11.4 Predictive Distributions of
FRV and FRSS 200 11.5 An Illustration 206 11.6 Problems 208 12 Stein
Estimation 209 12.1 Class of Estimators 210 12.2 Preliminaries and Some
Theorems 213 12.3 Superiority Conditions 216 12.4 Problems 223 References
225 Subject Index 243
Symbols xxiii 1 Introduction 1 1.1 Objective of the Book 1 1.2 Models Under
Consideration 3 2 Preliminaries 7 2.1 Normal distribution 8 2.2 Chisquare
distribution 8 2.3 Student's t distributions 10 2.4 F distribution 14 2.5
Multivariate Normal distribution 16 2.6 Multivariate t distribution 17 2.7
Problems 28 3 Location Model 31 3.1 Model Specification 32 3.2 Unbiased
Estimates of _ and _² and test of hypothesis 32 3.3 Estimators 36 3.4 Bias
and MSE Expressions of the Location Estimators 38 3.5 Various Estimates of
Variance 48 3.6 Problems 60 4 Simple Regression Model 61 4.1 Introduction
62 4.2 Estimation and Testing of _ 62 4.3 Properties of Intercept Parameter
66 4.4 Comparison 69 4.5 Numerical Illustration 72 4.6 Problems 77 5 ANOVA
79 5.1 Model Specification 80 5.2 Proposed Estimators and Testing 80 5.3
Bias, MSE and Risk Expressions 85 5.4 Risk Analysis 87 5.5 Problems 93 6
Parallelism Model 95 6.1 Model Specification 96 6.2 Estimation of the
Parameters and Test of Parallelism 97 6.3 Bias, MSE, and Risk Expressions
103 6.4 Risk Analysis 106 6.5 Problems 110 7 Multiple Regression Model 111
7.1 Model Specification 112 7.2 Shrinkage Estimators and Testing 112 7.3
Bias and Risk Expressions 116 7.4 Comparison 120 7.5 Problems 126 8 Ridge
Regression 127 8.1 Model Specification 128 8.2 Proposed Estimators 129 8.3
Bias, MSE, and Risk Expressions 130 8.4 Performance of the Estimators 135
8.5 Choice of Ridge Parameter 153 8.6 Problems 164 9 Multivariate Models
165 9.1 Location Model 166 9.2 Testing of Hypothesis and Several Estimators
of Local Parameter 167 9.3 Bias, Quadratic Bias, MSE, and Risk Expressions
169 9.4 Risk Analysis of the Estimators 171 9.5 Simple Multivariate Linear
Model 175 9.6 Problems 180 10 Bayesian Analysis 181 10.1 Introduction
(Zellner's Model) 181 10.2 Conditional Bayesian Inference 183 10.3 Matrix
Variate t Distribution 185 10.4 Bayesian Analysis in Multivariate
Regression Model 187 10.5 Problems 194 11 Linear Prediction Models 195 11.1
Model & Preliminaries 196 11.2 Distribution of SRV and RSS 197 11.3
Regression Model for Future Responses 199 11.4 Predictive Distributions of
FRV and FRSS 200 11.5 An Illustration 206 11.6 Problems 208 12 Stein
Estimation 209 12.1 Class of Estimators 210 12.2 Preliminaries and Some
Theorems 213 12.3 Superiority Conditions 216 12.4 Problems 223 References
225 Subject Index 243