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线性模型的参数估计和预测理论 目录
ContentsPrefaceChapter 1 Introduction 11.1 Research progress on parameter estimation 11.1.1 Advances in the estimation of regression coe±cient 11.1.2 Advances in the estimation of error variance 31.2 Research progress on-nite population 41.3 Plan of this book 5Chapter 2 Comparisons of Biased Estimators for Regression Coe±cient 72.1 Introduction 72.2 Balanced loss function and risk 92.3 Numerical analysis 122.4 Proof of main results 15Chapter 3 Comparisons of Parametric Estimation in a Misspeci-ed Linear Model 193.1 Comparisons of estimators for regression coe±cient 193.1.1 Introduction 193.1.2 Estimators and its risks 213.1.3 Comparisons of proposed estimators in theory 273.1.4 Comparisons of proposed estimators by numerical analysis 333.1.5 Simulation example 383.2 Comparisons of estimators for error variance 393.2.1 Introduction 393.2.2 Estimators and its risks 423.2.3 Analysis of the risks 453.2.4 The bootstrap 52Chapter 4 Comparisons of Preliminary Test Estimators Based on W， LR and LM Tests 554.1 Comparisons of pre-test estimators in a normal linear model 554.1.1 Introduction 554.1.2 Estimators and its risks 574.1.3 Comparison of proposed estimators 604.1.4 Simulation 654.2 Comparisons of pre-test estimators in a linear model with multivariate t distribution 674.2.1 Introduction 674.2.2 Risks of proposed estimators 694.2.3 Comparison in theory 724.2.4 Comparison by numerical analysis 754.2.5 Comparison by bootstrap method 77Chapter 5 Admissible Predictions for Finite Population Regression Coe±cient 805.1 Linear admissible prediction for a general-nite population 805.1.1 Introduction 805.1.2 Admissibility of a homogeneous linear predictor in the class of linear predictors 825.1.3 Admissibility of a homogeneous linear predictor in the class of all predictors 835.2 All linear admissible prediction in a-nite population with respect to inequality constraints 875.2.1 Introduction 875.2.2 Admissibility of linear predictors in LI on T1 905.2.3 Admissibility of linear predictors in L on T1 99Chapter 6 Minimax Predictions for Finite Population Regression Coe±cient 1046.1 Linear minimax prediction in a Gauss-Markov population 1046.1.1 Introduction 1046.1.2 Linear minimax predictor 1076.1.3 Admissibility of LMP 1156.1.4 Comparison of BLUP and LMP 1166.2 Linear minimax prediction in a normal-nite population 1186.2.1 Introduction 1186.2.2 Optimal predictor 1206.2.3 Minimax predictor 1236.2.4 Comparison of BUP and MP 1316.2.5 The SPP and comparison with BUP and MP 1336.3 Linear minimax prediction in a-nite population with ellipsoidal constraints 1346.3.1 Introduction 1346.3.2 Linear minimax prediction 1376.3.3 Admissibility of homogeneous linear minimax prediction 1426.3.4 Simulation study 1456.3.5 Analysis of real data 147Chapter 7 Bayesian Prediction for Finite Population Quantities 1497.1 Introduction 1497.2 Bayes prediction of population quantities 1517.3 Bayes prediction of linear quantities 1547.4 Bayes prediction of quadratic quantities 1567.5 Examples 157References 160
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