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Statistical inference for models with multivariate t-distributed errors /
"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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken, New Jersey :
Wiley,
[2014]
|
| Temas: | |
| Acceso en línea: | Texto completo (Requiere registro previo con correo institucional) |
MARC
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| 100 | 1 | |a Saleh, A. K. Md. Ehsanes, |e author. | |
| 245 | 1 | 0 | |a Statistical inference for models with multivariate t-distributed errors / |c A.K. Md. Ehsanes Saleh, Department of Mathematics and Statistics, Carleton University, Ottawa, Canada, M. Arashi, Department of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran, S.M.M. Tabatabaey, Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran. |
| 264 | 1 | |a Hoboken, New Jersey : |b Wiley, |c [2014] | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 520 | |a "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 "-- |c Provided by publisher. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record an. publisher; resource not viewed. | |
| 505 | 0 | |6 880-01 |a 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. | |
| 590 | |a O'Reilly |b O'Reilly Online Learning: Academic/Public Library Edition | ||
| 650 | 0 | |a Regression analysis. | |
| 650 | 0 | |a Multivariate analysis. | |
| 650 | 6 | |a Analyse de régression. | |
| 650 | 6 | |a Analyse multivariée. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x Regression Analysis. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x Bayesian Analysis. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x Multivariate Analysis. |2 bisacsh | |
| 650 | 7 | |a Multivariate analysis. |2 fast |0 (OCoLC)fst01029105 | |
| 650 | 7 | |a Regression analysis. |2 fast |0 (OCoLC)fst01432090 | |
| 700 | 1 | |a Arashi, M. |q (Mohammad), |d 1981- |e author. | |
| 700 | 1 | |a Tabatabaey, S. M. M., |e author. | |
| 776 | 0 | 8 | |i Print version: |a Saleh, A.K. Md. Ehsanes. |t Statistical inference for models with multivariate t-distributed errors. |d Hoboken, New Jersey : John Wiley & Sonsa, Inc., [2014] |z 9781118854051 |w (DLC) 2014007304 |
| 856 | 4 | 0 | |u https://learning.oreilly.com/library/view/~/9781118853962/?ar |z Texto completo (Requiere registro previo con correo institucional) |
| 880 | 0 | 0 | |6 505-01/(S |g Machine generated contents note: |g 1. |t Introduction -- |g 1.1. |t Objective of the Book -- |g 1.2. |t Models under Consideration -- |g 1.2.1. |t Location Model -- |g 1.2.2. |t Simple Linear Model -- |g 1.2.3. |t ANOVA Model -- |g 1.2.4. |t Parallelism Model -- |g 1.2.5. |t Multiple Regression Model -- |g 1.2.6. |t Ridge Regression -- |g 1.2.7. |t Multivariate Model -- |g 1.2.8. |t Simple Multivariate Linear Model -- |g 1.3. |t Organization of the Book -- |g 1.4. |t Problems -- |g 2. |t Preliminaries -- |g 2.1. |t Normal Distribution -- |g 2.2. |t Chi-Square Distribution -- |g 2.3. |t Student's t-Distribution -- |g 2.4. |t F-Distribution -- |g 2.5. |t Multivariate Normal Distribution -- |g 2.6. |t Multivariate t-Distribution -- |g 2.6.1. |t Expected Values of Functions of M(p)t (η, σ2Vp, γo)-Variables -- |g 2.6.2. |t Sampling Distribution of Quadratic Forms -- |g 2.6.3. |t Distribution of Linear Functions of t-Variables -- |g 2.7. |t Problems -- |g 3. |t Location Model -- |g 3.1. |t Model Specification -- |g 3.2. |t Unbiased Estimates of θ and σ2 and Test of Hypothesis -- |g 3.3. |t Estimators -- |g 3.4. |t Bias and MSE Expressions of the Location Estimators -- |g 3.4.1. |t Analysis of the Estimators of Location Parameter -- |g 3.5. |t Various Estimates of Variance -- |g 3.5.1. |t Bias and MSE Expressions of the Variance Estimators -- |g 3.5.2. |t Analysis of the Estimators of the Variance Parameter -- |g 3.6. |t Problems -- |g 4. |t Simple Regression Model -- |g 4.1. |t Introduction -- |g 4.2. |t Estimation and Testing of η -- |g 4.2.1. |t Estimation of η -- |g 4.2.2. |t Test of Intercept Parameter -- |g 4.2.3. |t Estimators of β and θ -- |g 4.3. |t Properties of Intercept Parameter -- |g 4.3.1. |t Bias Expressions of the Estimators -- |g 4.3.2. |t MSE Expressions of the Estimators -- |g 4.4. |t Comparison -- |g 4.4.1. |t Optimum Level of Significance of &θcirc;PTn -- |g 4.5. |t Numerical Illustration -- |g 4.6. |t Problems -- |g 5. |t Anova -- |g 5.1. |t Model Specification -- |g 5.2. |t Proposed Estimators and Testing -- |g 5.3. |t Bias, MSE, and Risk Expressions -- |g 5.4. |t Risk Analysis -- |g 5.4.1. |t Comparison of &θcirc;n and θn -- |g 5.4.2. |t Comparison of &θcirc;PTn and θn(&θcirc;n) -- |g 5.4.3. |t Comparison of &θcirc;Sn, θn, &θcirc;n, and &θcirc;PTn -- |g 5.4.4. |t Comparison of &θcirc;Sn and &θcirc;S+n -- |g 5.5. |t Problems -- |g 6. |t Parallelism Model -- |g 6.1. |t Model Specification -- |g 6.2. |t Estimation of the Parameters and Test of Parallelism -- |g 6.2.1. |t Test of Parallelism -- |g 6.3. |t Bias, MSE, and Risk Expressions -- |g 6.3.1. |t Expressions of Bias, MSE Matrix, and Risks of βn, n, &βcirc;n and [ˆ]n -- |g 6.3.2. |t Expressions of Bias, MSE Matrix, and Risks of the PTEs of β and -- |g 6.3.3. |t Expressions of Bias, MSE Matrix, and Risks of the SSEs of β and -- |g 6.3.4. |t Expressions of Bias, MSE Matrix, and Risks of the PRSEs of β and -- |g 6.4. |t Risk Analysis -- |g 6.5. |t Problems -- |g 7. |t Multiple Regression Model -- |g 7.1. |t Model Specification -- |g 7.2. |t Shrinkage Estimators and Testing -- |g 7.3. |t Bias and Risk Expressions -- |g 7.3.1. |t Balanced Loss Function -- |g 7.3.2. |t Properties -- |g 7.4. |t Comparison -- |g 7.5. |t Problems -- |g 8. |t Ridge Regression -- |g 8.1. |t Model Specification -- |g 8.2. |t Proposed Estimators -- |g 8.3. |t Bias, MSE, and Risk Expressions -- |g 8.3.1. |t Biases of the Estimators -- |g 8.3.2. |t MSE Matrices and Risks of the Estimators -- |g 8.4. |t Performance of the Estimators -- |g 8.4.1. |t Comparison between βn(k), &βcirc;Sn(k), and &βcirc;S+n(k) -- |g 8.4.2. |t Comparison between βn(k) and &βcirc;PTn(k) -- |g 8.4.3. |t Comparison between βn(k) and &βcirc;n -- |g 8.4.4. |t Comparison between &βcirc;n(k) and &βcirc;n -- |g 8.4.5. |t Comparison between &βcirc;PTn and &βcirc;PTn(k) -- |g 8.4.6. |t Comparison between &βcirc;Sn and &βcirc;Sn(k) -- |g 8.4.7. |t Comparison between &βcirc;S+n and &βcirc;S+n(k) -- |g 8.5. |t Choice of Ridge Parameter -- |g 8.5.1. |t Real Example -- |g 8.5.2. |t Simulation -- |g 8.6. |t Problems -- |g 9. |t Multivariate Models -- |g 9.1. |t Location Model -- |g 9.2. |t Testing of Hypothesis and Several Estimators of Local Parameter -- |g 9.3. |t Bias, Quadratic Bias, MSE, and Risk Expressions -- |g 9.4. |t Risk Analysis of the Estimators -- |g 9.4.1. |t Comparison between θN, &θcirc;N, and &θcirc;PTN -- |g 9.4.2. |t Comparison between θN, &θcirc;N, &θcirc;PTN, and &θcirc;SN -- |g 9.4.3. |t Comparison between θN, &θcirc;SN, and &θcirc;S+N -- |g 9.5. |t Simple Multivariate Linear Model -- |g 9.5.1. |t More Estimators for β and θ -- |g 9.5.2. |t Bias, Quadratic Bias, and MSE Expressions -- |g 9.6. |t Problems -- |g 10. |t Bayesian Analysis -- |g 10.1. |t Introduction (Zellner's Model) -- |g 10.2. |t Conditional Bayesian Inference -- |g 10.3. |t Matrix Variate t-Distribution -- |g 10.4. |t Bayesian Analysis in Multivariate Regression Model -- |g 10.4.1. |t Properties of B and Φ -- |g 10.5. |t Problems -- |g 11. |t Linear Prediction Models -- |g 11.1. |t Model and Preliminaries -- |g 11.2. |t Distribution of SRV and RSS -- |g 11.3. |t Regression Model for Future Responses -- |g 11.4. |t Predictive Distributions of FRV and FRSS -- |g 11.4.1. |t Distribution of the FRV -- |g 11.4.2. |t Distribution of Future Residual Sum of Squares -- |g 11.5. |t Illustration -- |g 11.6. |t Problems -- |g 12. |t Stein Estimation -- |g 12.1. |t Class of Estimators -- |g 12.1.1. |t Without Prior Information -- |g 12.1.2. |t Taking Prior Information -- |g 12.2. |t Preliminaries and Some Theorems -- |g 12.3. |t Superiority Conditions -- |g 12.3.1. |t Without Taking Prior Information -- |g 12.3.2. |t Taking Prior Information -- |g 12.4. |t Problems. |
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