线性模型是现代统计学中一类重要的模型，广泛地应用于经济，金融，生物、医学和工程技术等领域。在该模型的建模分析中，统计学家主要研究模型的参数估计理论，假设检验以及未来观察值的预测等统计推断问题。相比较，参数的假设检验以及未来观察值的预测问题研究更多的依赖于参数估计的结果。因此，模型的参数估计理论在整个建模分析过程中起到重要的作用，得到统计学家的高度重视。一方面，需要研究模型的参数估计理论和方法，并对各种估计的优良性进行分析；另一方面，需要基于模型参数估计结果对未来观察值的预测方法进行研究。本书围绕厚尾分布下线性模型中若干参数估计方法，基于统计决策理论对它们的优良性进行分析，便于人们合理的选择各种估计方法，同时分别基于统计决策理论和贝叶斯分析思想探讨有限总体的最优预测，可容许预测和贝叶斯预测。
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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
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