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Statistical Inference for Models with Multivariate t-Distributed Errors

Book Description

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

  • Table of Contents

    1. Cover
    2. Half Title page
    3. Title page
    4. Copyright page
    5. Dedication
    6. List of Figures
    7. List of Tables
    8. Preface
    9. Glossary
    10. List of Symbols
    11. Chapter 1: Introduction
      1. 1.1 Objective of the Book
      2. 1.2 Models under Consideration
      3. 1.3 Organization of the Book
      4. 1.4 Problems
    12. Chapter 2: Preliminaries
      1. 2.1 Normal Distribution
      2. 2.2 Chi-Square Distribution
      3. 2.3 Student’s t-Distribution
      4. 2.4 F-Distribution
      5. 2.5 Multivariate Normal Distribution
      6. 2.6 Multivariate t-Distribution
      7. 2.7 Problems
    13. Chapter 3: Location Model
      1. 3.1 Model Specification
      2. 3.2 Unbiased Estimates of θ and σ2 and Test of Hypothesis
      3. 3.3 Estimators
      4. 3.4 Bias and MSE Expressions of the Location Estimators
      5. 3.5 Various Estimates of Variance
      6. 3.6 Problems
    14. Chapter 4: Simple Regression Model
      1. 4.1 Introduction
      2. 4.2 Estimation and Testing of η
      3. 4.3 Properties of Intercept Parameter
      4. 4.4 Comparison
      5. 4.5 Numerical Illustration
      6. 4.6 Problems
    15. Chapter 5: Anova
      1. 5.1 Model Specification
      2. 5.2 Proposed Estimators and Testing
      3. 5.3 Bias, MSE, and Risk Expressions
      4. 5.4 Risk Analysis
      5. 5.5 Problems
    16. Chapter 6: Parallelism Model
      1. 6.1 Model Specification
      2. 6.2 Estimation of the Parameters and Test of Parallelism
      3. 6.3 Bias, MSE, and Risk Expressions
      4. 6.4 Risk Analysis
      5. 6.5 Problems
    17. Chapter 7: Multiple Regression Model
      1. 7.1 Model Specification
      2. 7.2 Shrinkage Estimators and Testing
      3. 7.3 Bias and Risk Expressions
      4. 7.4 Comparison
      5. 7.5 Problems
    18. Chapter 8: Ridge Regression
      1. 8.1 Model Specification
      2. 8.2 Proposed Estimators
      3. 8.3 Bias, MSE, and Risk Expressions
      4. 8.4 Performance of the Estimators
      5. 8.5 Choice of Ridge Parameter
      6. 8.6 Problems
    19. Chapter 9: Multivariate Models
      1. 9.1 Location Model
      2. 9.2 Testing of Hypothesis and Several Estimators of Local Parameter
      3. 9.3 Bias, Quadratic Bias, MSE, and Risk Expressions
      4. 9.4 Risk Analysis of the Estimators
      5. 9.5 Simple Multivariate Linear Model
      6. 9.6 Problems
    20. Chapter 10: Bayesian Analysis
      1. 10.1 Introduction (Zellner’s Model)
      2. 10.2 Conditional Bayesian Inference
      3. 10.3 Matrix Variate t-Distribution
      4. 10.4 Bayesian Analysis in Multivariate Regression Model
      5. 10.5 Problems
    21. Chapter 11: Linear Prediction Models
      1. 11.1 Model and Preliminaries
      2. 11.2 Distribution of SRV and RSS
      3. 11.3 Regression Model for Future Responses
      4. 11.4 Predictive Distributions of FRV and FRSS
      5. 11.5 An Illustration
      6. 11.6 Problems
    22. Chapter 12: Stein Estimation
      1. 12.1 Class of Estimators
      2. 12.2 Preliminaries and Some Theorems
      3. 12.3 Superiority Conditions
      4. 12.4 Problems
    23. References
    24. Author Index
    25. Subject Index