線性模型是現代統計學中一類重要的模型，廣泛地應用于經濟，金融，生物、醫學和工程技術等領域。在該模型的建模分析中，統計學家主要研究模型的參數估計理論，假設檢驗以及未來觀察值的預測等統計推斷問題。相比較，參數的假設檢驗以及未來觀察值的預測問題研究更多的依賴於參數估計的結果。
 
因此，模型的參數估計理論在整個建模分析過程中起到重要的作用，得到統計學家的高度重視。一方面，需要研究模型的參數估計理論和方法，並對各種估計的優良性進行分析；另一方面，需要基於模型參數估計結果對未來觀察值的預測方法進行研究。
 
本書圍繞厚尾分佈下線性模型中若干參數估計方法，基於統計決策理論對它們的優良性進行分析，便於人們合理的選擇各種估計方法，同時分別基於統計決策理論和貝葉斯分析思想探討有限總體的最優預測，可容許預測和貝葉斯預測。


Contents

Preface

Chapter 1 Introduction 1
1.1 Research progress on parameter estimation 1
1.1.1 Advances in the estimation of regression coe±cient 1
1.1.2 Advances in the estimation of error variance 3
1.2 Research progress on-nite population 4
1.3 Plan of this book 5

Chapter 2 Comparisons of Biased Estimators for Regression Coe±cient 7
2.1 Introduction 7
2.2 Balanced loss function and risk 9
2.3 Numerical analysis 12
2.4 Proof of main results 15

Chapter 3 Comparisons of Parametric Estimation in a Misspeci-ed Linear Model 19
3.1 Comparisons of estimators for regression coe±cient 19
3.1.1 Introduction 19
3.1.2 Estimators and its risks 21
3.1.3 Comparisons of proposed estimators in theory 27
3.1.4 Comparisons of proposed estimators by numerical analysis 33
3.1.5 Simulation example 38
3.2 Comparisons of estimators for error variance 39
3.2.1 Introduction 39
3.2.2 Estimators and its risks 42
3.2.3 Analysis of the risks 45
3.2.4 The bootstrap 52

Chapter 4 Comparisons of Preliminary Test Estimators Based on W， LR and LM Tests 55
4.1 Comparisons of pre-test estimators in a normal linear model 55
4.1.1 Introduction 55
4.1.2 Estimators and its risks 57
4.1.3 Comparison of proposed estimators 60
4.1.4 Simulation 65
4.2 Comparisons of pre-test estimators in a linear model with multivariate t distribution 67
4.2.1 Introduction 67
4.2.2 Risks of proposed estimators 69
4.2.3 Comparison in theory 72
4.2.4 Comparison by numerical analysis 75
4.2.5 Comparison by bootstrap method 77

Chapter 5 Admissible Predictions for Finite Population Regression Coe±cient 80
5.1 Linear admissible prediction for a general-nite population 80
5.1.1 Introduction 80
5.1.2 Admissibility of a homogeneous linear predictor in the class of linear predictors 82
5.1.3 Admissibility of a homogeneous linear predictor in the class of all predictors 83
5.2 All linear admissible prediction in a-nite population with respect to inequality constraints 87
5.2.1 Introduction 87
5.2.2 Admissibility of linear predictors in LI on T1 90
5.2.3 Admissibility of linear predictors in L on T1 99

Chapter 6 Minimax Predictions for Finite Population Regression Coe±cient 104
6.1 Linear minimax prediction in a Gauss-Markov population 104
6.1.1 Introduction 104
6.1.2 Linear minimax predictor 107
6.1.3 Admissibility of LMP 115
6.1.4 Comparison of BLUP and LMP 116
6.2 Linear minimax prediction in a normal-nite population 118
6.2.1 Introduction 118
6.2.2 Optimal predictor 120
6.2.3 Minimax predictor 123
6.2.4 Comparison of BUP and MP 131
6.2.5 The SPP and comparison with BUP and MP 133
6.3 Linear minimax prediction in a-nite population with ellipsoidal constraints 134
6.3.1 Introduction 134
6.3.2 Linear minimax prediction 137
6.3.3 Admissibility of homogeneous linear minimax prediction 142
6.3.4 Simulation study 145
6.3.5 Analysis of real data 147

Chapter 7 Bayesian Prediction for Finite Population Quantities 149
7.1 Introduction 149
7.2 Bayes prediction of population quantities 151
7.3 Bayes prediction of linear quantities 154
7.4 Bayes prediction of quadratic quantities 156
7.5 Examples 157
References 160