Statistical inference for models with multivariate t-distributed errors / / A. K. Md. Ehsanes Saleh, M. Arashi, S. M. M. Tabatabaey

• Record Nr.: UNINA9910132350603321
• Autore: Saleh A. K. Md. Ehsanes
• Pubbl/distr/stampa: Hoboken, New Jersey : , : John Wiley & Sons, , 2014; ©2014
• ISBN: 1-118-85396-2; 1-118-85392-X; 1-118-85393-8
• Edizione: [1st edition]
• Descrizione fisica: 1 online resource (275 p.)
• Classificazione: MAT029030MAT029010MAT029020
• Disciplina: 519.536
• Soggetti: Regression analysis; Multivariate analysis
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and indexes.
• Nota di contenuto: 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; 2.5 Multivariate Normal Distribution2.6 Multivariate t-Distribution; 2.6.1 Expected Values of Functions of M_t^(p)(η , σ^2V_p, 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 σ^2 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 Parameter3.6 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 θ_n^PT; 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 θ_n and θ_n5.4.2 Comparison of θ_n_PT and θ_n(θ_n); 5.4.3 Comparison of θ_n^S, θ_n , θn, and θ_n^PT; 5.4.4 Comparison of θ_n^S and θ_n^S+; 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 β_n, Θ_n, β_n, and Θ_n; 6.3.2 Expressions of Bias, MSE Matrix, and Risks of the PTEs of β and Θ; 6.3.3 Expressions of Bias, MSE Matrix, and Risks of the SSEs of β and Θ; 6.3.4 Expressions of Bias, MSE Matrix, and Risks of the PRSEs of β and Θ6.4 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 β_n(k), β_n^S(k), and β_n^S+(k); 8.4.2 Comparison between β_n (k) and β_n^PT (k)
• Sommario/riassunto: "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 "--