| Description |
1 online resource |
| Summary |
"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 "-- Provided by publisher. |
| Bibliography |
Includes bibliographical references and index. |
| Contents |
Cover; 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. |
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Machine generated contents note: 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 -- 2.5. Multivariate Normal Distribution -- 2.6. Multivariate t-Distribution -- 2.6.1. Expected Values of Functions of M(p)t (η, σ2Vp, γo)-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 θ and σ2 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 -- 3.5.2. Analysis of the Estimators of the Variance Parameter -- 3.6. Problems -- 4. Simple Regression Model -- 4.1. Introduction -- 4.2. Estimation and Testing of η -- 4.2.1. Estimation of η -- 4.2.2. Test of Intercept Parameter -- 4.2.3. Estimators of β and θ -- 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 &θcirc;PTn -- 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 -- 5.4.1. Comparison of &θcirc;n and θn -- 5.4.2. Comparison of &θcirc;PTn and θn(&θcirc;n) -- 5.4.3. Comparison of &θcirc;Sn, θn, &θcirc;n, and &θcirc;PTn -- 5.4.4. Comparison of &θcirc;Sn and &θcirc;S+n -- 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 βn, n, &βcirc;n and [ˆ]n -- 6.3.2. Expressions of Bias, MSE Matrix, and Risks of the PTEs of β and -- 6.3.3. Expressions of Bias, MSE Matrix, and Risks of the SSEs of β and -- 6.3.4. Expressions of Bias, MSE Matrix, and Risks of the PRSEs of β 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 βn(k), &βcirc;Sn(k), and &βcirc;S+n(k) -- 8.4.2. Comparison between βn(k) and &βcirc;PTn(k) -- 8.4.3. Comparison between βn(k) and &βcirc;n -- 8.4.4. Comparison between &βcirc;n(k) and &βcirc;n -- 8.4.5. Comparison between &βcirc;PTn and &βcirc;PTn(k) -- 8.4.6. Comparison between &βcirc;Sn and &βcirc;Sn(k) -- 8.4.7. Comparison between &βcirc;S+n and &βcirc;S+n(k) -- 8.5. Choice of Ridge Parameter -- 8.5.1. Real Example -- 8.5.2. Simulation -- 8.6. Problems -- 9. Multivariate Models -- 9.1. Location Model -- 9.2. Testing of Hypothesis and Several Estimators of Local Parameter -- 9.3. Bias, Quadratic Bias, MSE, and Risk Expressions -- 9.4. Risk Analysis of the Estimators -- 9.4.1. Comparison between θN, &θcirc;N, and &θcirc;PTN -- 9.4.2. Comparison between θN, &θcirc;N, &θcirc;PTN, and &θcirc;SN -- 9.4.3. Comparison between θN, &θcirc;SN, and &θcirc;S+N -- 9.5. Simple Multivariate Linear Model -- 9.5.1. More Estimators for β and θ -- 9.5.2. Bias, Quadratic Bias, and MSE Expressions -- 9.6. Problems -- 10. Bayesian Analysis -- 10.1. Introduction (Zellner's Model) -- 10.2. Conditional Bayesian Inference -- 10.3. Matrix Variate t-Distribution -- 10.4. Bayesian Analysis in Multivariate Regression Model -- 10.4.1. Properties of B and Φ -- 10.5. Problems -- 11. Linear Prediction Models -- 11.1. Model and Preliminaries -- 11.2. Distribution of SRV and RSS -- 11.3. Regression Model for Future Responses -- 11.4. Predictive Distributions of FRV and FRSS -- 11.4.1. Distribution of the FRV -- 11.4.2. Distribution of Future Residual Sum of Squares -- 11.5. Illustration -- 11.6. Problems -- 12. Stein Estimation -- 12.1. Class of Estimators -- 12.1.1. Without Prior Information -- 12.1.2. Taking Prior Information -- 12.2. Preliminaries and Some Theorems -- 12.3. Superiority Conditions -- 12.3.1. Without Taking Prior Information -- 12.3.2. Taking Prior Information -- 12.4. Problems. |
| Subject |
Regression analysis.
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Multivariate analysis.
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Analyse de régression. |
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Analyse multivariée. |
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Multivariate analysis |
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Regression analysis |
| Added Author |
Arashi, M. (Mohammad), 1981- author.
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Tabatabaey, S. M. M., author.
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| Other Form: |
Print version: Saleh, A.K. Md. Ehsanes. Statistical inference for models with multivariate t-distributed errors. Hoboken, New Jersey : John Wiley & Sonsa, Inc., [2014] 9781118854051 (DLC) 2014007304 |
| ISBN |
9781118853962 (epub) |
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1118853962 (epub) |
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9781118853924 (pdf) |
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111885392X (pdf) |
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9781118853931 (electronic bk.) |
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1118853938 (electronic bk.) |
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1118854055 (hardback) |
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9781118854051 (hardback) |
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9781322196138 (MyiLibrary) |
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1322196133 (MyiLibrary) |
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(hardback) |
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