Statistical Inference for Models with Multivariate t-Distributed Errors
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Statistical Inference for Models with Multivariate t-Distributed Errors
Saleh, A. K. Md. Ehsanes; Arashi, Mohammad; Tabatabaey, S M M
John Wiley & Sons Inc
10/2014
272
Dura
Inglês
9781118854051
15 a 20 dias
508
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List of Figures xv
List of Tables xvii
Preface xix
Glossary xxi
List of Symbols xxiii
1 Introduction 1
1.1 Objective of the Book 1
1.2 Models Under Consideration 3
2 Preliminaries 7
2.1 Normal distribution 8
2.2 Chisquare distribution 8
2.3 Student's t distributions 10
2.4 F distribution 14
2.5 Multivariate Normal distribution 16
2.6 Multivariate t distribution 17
2.7 Problems 28
3 Location Model 31
3.1 Model Specification 32
3.2 Unbiased Estimates of _ and _2 and test of hypothesis 32
3.3 Estimators 36
3.4 Bias and MSE Expressions of the Location Estimators 38
3.5 Various Estimates of Variance 48
3.6 Problems 60
4 Simple Regression Model 61
4.1 Introduction 62
4.2 Estimation and Testing of _ 62
4.3 Properties of Intercept Parameter 66
4.4 Comparison 69
4.5 Numerical Illustration 72
4.6 Problems 77
5 ANOVA 79
5.1 Model Specification 80
5.2 Proposed Estimators and Testing 80
5.3 Bias, MSE and Risk Expressions 85
5.4 Risk Analysis 87
5.5 Problems 93
6 Parallelism Model 95
6.1 Model Specification 96
6.2 Estimation of the Parameters and Test of Parallelism 97
6.3 Bias, MSE, and Risk Expressions 103
6.4 Risk Analysis 106
6.5 Problems 110
7 Multiple Regression Model 111
7.1 Model Specification 112
7.2 Shrinkage Estimators and Testing 112
7.3 Bias and Risk Expressions 116
7.4 Comparison 120
7.5 Problems 126
8 Ridge Regression 127
8.1 Model Specification 128
8.2 Proposed Estimators 129
8.3 Bias, MSE, and Risk Expressions 130
8.4 Performance of the Estimators 135
8.5 Choice of Ridge Parameter 153
8.6 Problems 164
9 Multivariate Models 165
9.1 Location Model 166
9.2 Testing of Hypothesis and Several Estimators of Local Parameter 167
9.3 Bias, Quadratic Bias, MSE, and Risk Expressions 169
9.4 Risk Analysis of the Estimators 171
9.5 Simple Multivariate Linear Model 175
9.6 Problems 180
10 Bayesian Analysis 181
10.1 Introduction (Zellner's Model) 181
10.2 Conditional Bayesian Inference 183
10.3 Matrix Variate t Distribution 185
10.4 Bayesian Analysis in Multivariate Regression Model 187
10.5 Problems 194
11 Linear Prediction Models 195
11.1 Model & Preliminaries 196
11.2 Distribution of SRV and RSS 197
11.3 Regression Model for Future Responses 199
11.4 Predictive Distributions of FRV and FRSS 200
11.5 An Illustration 206
11.6 Problems 208
12 Stein Estimation 209
12.1 Class of Estimators 210
12.2 Preliminaries and Some Theorems 213
12.3 Superiority Conditions 216
12.4 Problems 223
References 225
Subject Index 243
List of Tables xvii
Preface xix
Glossary xxi
List of Symbols xxiii
1 Introduction 1
1.1 Objective of the Book 1
1.2 Models Under Consideration 3
2 Preliminaries 7
2.1 Normal distribution 8
2.2 Chisquare distribution 8
2.3 Student's t distributions 10
2.4 F distribution 14
2.5 Multivariate Normal distribution 16
2.6 Multivariate t distribution 17
2.7 Problems 28
3 Location Model 31
3.1 Model Specification 32
3.2 Unbiased Estimates of _ and _2 and test of hypothesis 32
3.3 Estimators 36
3.4 Bias and MSE Expressions of the Location Estimators 38
3.5 Various Estimates of Variance 48
3.6 Problems 60
4 Simple Regression Model 61
4.1 Introduction 62
4.2 Estimation and Testing of _ 62
4.3 Properties of Intercept Parameter 66
4.4 Comparison 69
4.5 Numerical Illustration 72
4.6 Problems 77
5 ANOVA 79
5.1 Model Specification 80
5.2 Proposed Estimators and Testing 80
5.3 Bias, MSE and Risk Expressions 85
5.4 Risk Analysis 87
5.5 Problems 93
6 Parallelism Model 95
6.1 Model Specification 96
6.2 Estimation of the Parameters and Test of Parallelism 97
6.3 Bias, MSE, and Risk Expressions 103
6.4 Risk Analysis 106
6.5 Problems 110
7 Multiple Regression Model 111
7.1 Model Specification 112
7.2 Shrinkage Estimators and Testing 112
7.3 Bias and Risk Expressions 116
7.4 Comparison 120
7.5 Problems 126
8 Ridge Regression 127
8.1 Model Specification 128
8.2 Proposed Estimators 129
8.3 Bias, MSE, and Risk Expressions 130
8.4 Performance of the Estimators 135
8.5 Choice of Ridge Parameter 153
8.6 Problems 164
9 Multivariate Models 165
9.1 Location Model 166
9.2 Testing of Hypothesis and Several Estimators of Local Parameter 167
9.3 Bias, Quadratic Bias, MSE, and Risk Expressions 169
9.4 Risk Analysis of the Estimators 171
9.5 Simple Multivariate Linear Model 175
9.6 Problems 180
10 Bayesian Analysis 181
10.1 Introduction (Zellner's Model) 181
10.2 Conditional Bayesian Inference 183
10.3 Matrix Variate t Distribution 185
10.4 Bayesian Analysis in Multivariate Regression Model 187
10.5 Problems 194
11 Linear Prediction Models 195
11.1 Model & Preliminaries 196
11.2 Distribution of SRV and RSS 197
11.3 Regression Model for Future Responses 199
11.4 Predictive Distributions of FRV and FRSS 200
11.5 An Illustration 206
11.6 Problems 208
12 Stein Estimation 209
12.1 Class of Estimators 210
12.2 Preliminaries and Some Theorems 213
12.3 Superiority Conditions 216
12.4 Problems 223
References 225
Subject Index 243
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students; uniquely; tdistributed; models statistical inference; presents systematic; linear; multivariate; analytical; errors; statistical; development; models; fields including; book; mathematics; variety; applications; physical
List of Figures xv
List of Tables xvii
Preface xix
Glossary xxi
List of Symbols xxiii
1 Introduction 1
1.1 Objective of the Book 1
1.2 Models Under Consideration 3
2 Preliminaries 7
2.1 Normal distribution 8
2.2 Chisquare distribution 8
2.3 Student's t distributions 10
2.4 F distribution 14
2.5 Multivariate Normal distribution 16
2.6 Multivariate t distribution 17
2.7 Problems 28
3 Location Model 31
3.1 Model Specification 32
3.2 Unbiased Estimates of _ and _2 and test of hypothesis 32
3.3 Estimators 36
3.4 Bias and MSE Expressions of the Location Estimators 38
3.5 Various Estimates of Variance 48
3.6 Problems 60
4 Simple Regression Model 61
4.1 Introduction 62
4.2 Estimation and Testing of _ 62
4.3 Properties of Intercept Parameter 66
4.4 Comparison 69
4.5 Numerical Illustration 72
4.6 Problems 77
5 ANOVA 79
5.1 Model Specification 80
5.2 Proposed Estimators and Testing 80
5.3 Bias, MSE and Risk Expressions 85
5.4 Risk Analysis 87
5.5 Problems 93
6 Parallelism Model 95
6.1 Model Specification 96
6.2 Estimation of the Parameters and Test of Parallelism 97
6.3 Bias, MSE, and Risk Expressions 103
6.4 Risk Analysis 106
6.5 Problems 110
7 Multiple Regression Model 111
7.1 Model Specification 112
7.2 Shrinkage Estimators and Testing 112
7.3 Bias and Risk Expressions 116
7.4 Comparison 120
7.5 Problems 126
8 Ridge Regression 127
8.1 Model Specification 128
8.2 Proposed Estimators 129
8.3 Bias, MSE, and Risk Expressions 130
8.4 Performance of the Estimators 135
8.5 Choice of Ridge Parameter 153
8.6 Problems 164
9 Multivariate Models 165
9.1 Location Model 166
9.2 Testing of Hypothesis and Several Estimators of Local Parameter 167
9.3 Bias, Quadratic Bias, MSE, and Risk Expressions 169
9.4 Risk Analysis of the Estimators 171
9.5 Simple Multivariate Linear Model 175
9.6 Problems 180
10 Bayesian Analysis 181
10.1 Introduction (Zellner's Model) 181
10.2 Conditional Bayesian Inference 183
10.3 Matrix Variate t Distribution 185
10.4 Bayesian Analysis in Multivariate Regression Model 187
10.5 Problems 194
11 Linear Prediction Models 195
11.1 Model & Preliminaries 196
11.2 Distribution of SRV and RSS 197
11.3 Regression Model for Future Responses 199
11.4 Predictive Distributions of FRV and FRSS 200
11.5 An Illustration 206
11.6 Problems 208
12 Stein Estimation 209
12.1 Class of Estimators 210
12.2 Preliminaries and Some Theorems 213
12.3 Superiority Conditions 216
12.4 Problems 223
References 225
Subject Index 243
List of Tables xvii
Preface xix
Glossary xxi
List of Symbols xxiii
1 Introduction 1
1.1 Objective of the Book 1
1.2 Models Under Consideration 3
2 Preliminaries 7
2.1 Normal distribution 8
2.2 Chisquare distribution 8
2.3 Student's t distributions 10
2.4 F distribution 14
2.5 Multivariate Normal distribution 16
2.6 Multivariate t distribution 17
2.7 Problems 28
3 Location Model 31
3.1 Model Specification 32
3.2 Unbiased Estimates of _ and _2 and test of hypothesis 32
3.3 Estimators 36
3.4 Bias and MSE Expressions of the Location Estimators 38
3.5 Various Estimates of Variance 48
3.6 Problems 60
4 Simple Regression Model 61
4.1 Introduction 62
4.2 Estimation and Testing of _ 62
4.3 Properties of Intercept Parameter 66
4.4 Comparison 69
4.5 Numerical Illustration 72
4.6 Problems 77
5 ANOVA 79
5.1 Model Specification 80
5.2 Proposed Estimators and Testing 80
5.3 Bias, MSE and Risk Expressions 85
5.4 Risk Analysis 87
5.5 Problems 93
6 Parallelism Model 95
6.1 Model Specification 96
6.2 Estimation of the Parameters and Test of Parallelism 97
6.3 Bias, MSE, and Risk Expressions 103
6.4 Risk Analysis 106
6.5 Problems 110
7 Multiple Regression Model 111
7.1 Model Specification 112
7.2 Shrinkage Estimators and Testing 112
7.3 Bias and Risk Expressions 116
7.4 Comparison 120
7.5 Problems 126
8 Ridge Regression 127
8.1 Model Specification 128
8.2 Proposed Estimators 129
8.3 Bias, MSE, and Risk Expressions 130
8.4 Performance of the Estimators 135
8.5 Choice of Ridge Parameter 153
8.6 Problems 164
9 Multivariate Models 165
9.1 Location Model 166
9.2 Testing of Hypothesis and Several Estimators of Local Parameter 167
9.3 Bias, Quadratic Bias, MSE, and Risk Expressions 169
9.4 Risk Analysis of the Estimators 171
9.5 Simple Multivariate Linear Model 175
9.6 Problems 180
10 Bayesian Analysis 181
10.1 Introduction (Zellner's Model) 181
10.2 Conditional Bayesian Inference 183
10.3 Matrix Variate t Distribution 185
10.4 Bayesian Analysis in Multivariate Regression Model 187
10.5 Problems 194
11 Linear Prediction Models 195
11.1 Model & Preliminaries 196
11.2 Distribution of SRV and RSS 197
11.3 Regression Model for Future Responses 199
11.4 Predictive Distributions of FRV and FRSS 200
11.5 An Illustration 206
11.6 Problems 208
12 Stein Estimation 209
12.1 Class of Estimators 210
12.2 Preliminaries and Some Theorems 213
12.3 Superiority Conditions 216
12.4 Problems 223
References 225
Subject Index 243
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
