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 xvList of Tables xviiPreface xixGlossary xxiList of Symbols xxiii1 Introduction 11.1 Objective of the Book 11.2 Models Under Consideration 32 Preliminaries 72.1 Normal distribution 82.2 Chisquare distribution 82.3 Student’s t distributions 102.4 F distribution 142.5 Multivariate Normal distribution 162.6 Multivariate t distribution 172.7 Problems 283 Location Model 313.1 Model Specification 323.2 Unbiased Estimates of _ and _2 and test of hypothesis 323.3 Estimators 363.4 Bias and MSE Expressions of the Location Estimators 383.5 Various Estimates of Variance 483.6 Problems 604 Simple Regression Model 614.1 Introduction 624.2 Estimation and Testing of _ 624.3 Properties of Intercept Parameter 664.4 Comparison 694.5 Numerical Illustration 724.6 Problems 775 ANOVA 795.1 Model Specification 805.2 Proposed Estimators and Testing 805.3 Bias, MSE and Risk Expressions 855.4 Risk Analysis 875.5 Problems 936 Parallelism Model 956.1 Model Specification 966.2 Estimation of the Parameters and Test of Parallelism 976.3 Bias, MSE, and Risk Expressions 1036.4 Risk Analysis 1066.5 Problems 1107 Multiple Regression Model 1117.1 Model Specification 1127.2 Shrinkage Estimators and Testing 1127.3 Bias and Risk Expressions 1167.4 Comparison 1207.5 Problems 1268 Ridge Regression 1278.1 Model Specification 1288.2 Proposed Estimators 1298.3 Bias, MSE, and Risk Expressions 1308.4 Performance of the Estimators 1358.5 Choice of Ridge Parameter 1538.6 Problems 1649 Multivariate Models 1659.1 Location Model 1669.2 Testing of Hypothesis and Several Estimators of Local Parameter 1679.3 Bias, Quadratic Bias, MSE, and Risk Expressions 1699.4 Risk Analysis of the Estimators 1719.5 Simple Multivariate Linear Model 1759.6 Problems 18010 Bayesian Analysis 18110.1 Introduction (Zellner’s Model) 18110.2 Conditional Bayesian Inference 18310.3 Matrix Variate t Distribution 18510.4 Bayesian Analysis in Multivariate Regression Model 18710.5 Problems 19411 Linear Prediction Models 19511.1 Model & Preliminaries 19611.2 Distribution of SRV and RSS 19711.3 Regression Model for Future Responses 19911.4 Predictive Distributions of FRV and FRSS 20011.5 An Illustration 20611.6 Problems 20812 Stein Estimation 20912.1 Class of Estimators 21012.2 Preliminaries and Some Theorems 21312.3 Superiority Conditions 21612.4 Problems 223References 225Subject Index 243

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