Statistical Inference for Models with Multivariate t-Distributed Errors
Published on 1. October 2014
320 pages
978-1-118-85392-4 (ISBN)
Description
This book summarizes the results of various models under normaltheory with a brief review of the literature. StatisticalInference for Models with Multivariate t-DistributedErrors:
* Includes a wide array of applications for the analysis ofmultivariate observations
* Emphasizes the development of linear statistical models withapplications to engineering, the physical sciences, andmathematics
* Contains an up-to-date bibliography featuring the latest trendsand advances in the field to provide a collective source forresearch on the topic
* Addresses linear regression models with non-normal errors withpractical real-world examples
* Uniquely addresses regression models inStudent's t-distributed errorsand t-models
* Supplemented with an Instructor's Solutions Manual, which isavailable via written request by the Publisher
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A. K. Md. Ehsanes Saleh | Mohammad Arashi | S. M. M. Tabatabaey
Statistical Inference for Models with Multivariate t-Distributed Errors
Book
10/2014
Wiley
€118.50
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A. K. Md. Ehsanes Saleh | Mohammad Arashi | S. M. M. Tabatabaey
Statistical Inference for Models with Multivariate t-Distributed Errors
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10/2014
Wiley
€121.43
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Persons
A. K. Md. Ehsanes Saleh, PhD,is Professor Emeritus and Distinguished ResearchProfessor in the School of Mathematics and Statistics at CarletonUniversity, Canada. He has published well-over 200journal articles, and his research interests includenonparametric statistics, order statistics, and robust estimation. Dr. Saleh is a Fellow of the Institute of MathematicalStatistics, the American Statistical Association, and theBangladesh Academy of Sciences.
M. Arashi, PhD, is Associate Professor in theDepartment of Statistics at Shahrood University of Technology,Iran. The recipient of the Award for Teaching Excellence fromShahrood University in 2013, his research interests includeshrinkage estimation, distribution theory, and multivariateanalysis.
S. M. M. Tabatabaey, PhD, is Associate Professorin the Department of Statistics at Ferdowski University of Mashhad,Iran. The author of over fifteen journal articles, he is alsoa member of the Institute of Mathematical Statistics and theIranian Statistical Society.
Content
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 andtest 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 Parameter167
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
