Prediction Theory for Finite Populations

Synopsis.- 1. Basic Ideas and Principles.- 1.1. The Fixed Finite Population Model.- 1.2. The Superpopulation Model.- 1.2.1. The Regression Model.- 1.3. Predictors of Population Quantities.- 1.4. The Model—Based Design—Based Approach.- 1.5. Exercises.- 2. Optimal Predictors of Population Quantities.- 2.1. Best Linear Unbiased Predictors.- 2.2. Best Unbiased Predictors.- 2.3. Equivariant Predictors.- 2.3.1. A General Formulation.- 2.3.2. Location Equivariant Predictors of T Under Model SM1.- 2.3.3. Location Equivariant Predictors of T Under the Regression Model.- 2.3.4. Scale Equivariant Predictors of T.- 2.3.5. Location—Scale Equivariant Predictors of T.- 2.3.6. Location—Scale Equivariant Predictors of Sy2.- 2.4. Stein—Type Shrinkage Predictors.- 2.5. Exercises.- 3. Bayes and Minimax Predictors.- 3.1. The Multivariate Normal Model.- 3.1.1. Bayes Predictors of T.- 3.1.2. Bayes Predictors of ?N.- 3.1.3. Bayes Predictors of Sy2.- 3.2. Bayes Linear Predictors.- 3.3. Minimax and Admissible Predictors.- 3.4. Dynamic Bayesian Prediction.- 3.4.1. The Multinormal Dynamic Model.- 3.4.1.1. Dynamic Prediction of Tt.- 3.4.1.2. Dynamic Prediction of Sty2.- 3.5. Empirical Bayes Predictors.- 3.6. Exercises.- 4. Maximum—Likelihood Predictors.- 4.1. Predictive Likelihoods.- 4.1.1. Estimative Predictive Likelihoods.- 4.1.2. Profile Predictive Likelihoods.- 4.1.3. The Lauritzen—Hinkley Predictive Likelihoods.- 4.1.4. The Royall Predictive Likelihoods.- 4.2. Maximum Likelihood Predictors of T Under the Normal Superpopulation Model.- 4.2.1. Estimative Likelihood Predictors.- 4.2.2. Profile Likelihood Predictors.- 4.2.3. The LH Likelihood Predictors.- 4.2.4. The Royall Maximum—Likelihood Predictors.- 4.3. Maximum—Likelihood Predictors of the Population Variance Sy2 Under the Normal Regression Model.- 4.3.1. Estimative Likelihood Predictors.- 4.3.2. Profile Likelihood Predictors.- 4.3.3. LH Likelihood Predictors.- 4.4. Exercises.- 5. Classical and Bayesian Prediction Intervals.- 5.1. Confidence Prediction Intervals.- 5.2. Tolerance Prediction Intervals for T.- 5.3. Bayesian Prediction Intervals.- 5.4. Exercises.- 6. The Effects of Model Misspecification, Conditions For Robustness, and Bayesian Modeling.- 6.1. Robust Linear Prediction of T.- 6.2. Estimation of the Prediction Variance.- 6.3. Simulation Estimates of the ?* MSE of $${\hat T_R}$$.- 6.4. Bayesian Robustness.- 6.5. Bayesian Modeling.- 6.5.1. The Framework.- 6.5.2. The Normal Linear Model.- 6.6. Exercises.- 7. Models with Measurement Errors.- 7.1. The Location and Simple Regression Models.- 7.1.1. Model SM1.- 7.1.2. Simple Regression Model.- 7.1.3. Regression Type Predictors.- 7.2. Bayesian Models with Measurement Errors.- 7.2.1. Model SM1.- 7.2.2. Model SM6.- 7.2.3. Simple Regression Model.- 7.2.4. Orthogonal Transformations.- 7.3. Exercises.- 8. Asymptotic Properties in Finite Populations.- 8.1. Predictors of T.- 8.2. The Asymptotic Distribution of $${\hat \beta _{{s_k}}}$$.- 8.3. The Linear Regression Model with Measurement Errors.- 8.4. Exercises.- 9. Design Characteristics of Predictors.- 9.1. The QR Class of Predictors.- 9.2. ADU Predictors.- 9.3. Optimal ADU Predictors.- 9.4. Exercises.- Glossary of Predictors.- Author Index.