Minimax Solutions in Sampling from Finite Populations
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1: Decision Theoretic Foundations in Survey Sampling.- 1.1 General Definitions in Survey Sampling.- 1.2 Examples of Sampling Strategies.- 1.3 Classes of Strategies.- 1.4 Admissible Strategies.- 1.5 Superpopulation Models and Blu Predictors.- 1.6 Bayes Estimators.- 1.7 Minimax Strategies.- 1.8 A Modified Minimax Rule.- 1.9 Conditional Minimax Rules.- 1.10 Supplements.- 2: Minimax Solutions in Permutation Invariant Parameter Spaces.- 2.1 The Permutation Model.- 2.2 Supplements and Generalizations.- 3: The Cuboid as Parameter Space.- 3.1 The Scott Smith Solution.- 3.2 Lover Bounds.- 3.3 Some Spec...
1: Decision Theoretic Foundations in Survey Sampling.- 1.1 General Definitions in Survey Sampling.- 1.2 Examples of Sampling Strategies.- 1.3 Classes of Strategies.- 1.4 Admissible Strategies.- 1.5 Superpopulation Models and Blu Predictors.- 1.6 Bayes Estimators.- 1.7 Minimax Strategies.- 1.8 A Modified Minimax Rule.- 1.9 Conditional Minimax Rules.- 1.10 Supplements.- 2: Minimax Solutions in Permutation Invariant Parameter Spaces.- 2.1 The Permutation Model.- 2.2 Supplements and Generalizations.- 3: The Cuboid as Parameter Space.- 3.1 The Scott Smith Solution.- 3.2 Lover Bounds.- 3.3 Some Special Cases.- 3.4 Representative Minimax Solutions.- 3.5 Unbiased Minimax Solutions.- 3.6 Conditional Minimax Estimators.- 4: The HH- Space as Parameter Space.- 4.1 HT- Strategy Versus HH- Strategy.- 4.2 Conditions for a Gain in Efficiency.- 4.3 Minimax Solutions Using the HT- Estimator.- 4.4 Modified Minimax Solutions Using the HT- Estimator.- 4.5 Minimax Solutions in General Classes of Strategies.- 5: The Generalized HH- Space as Parameter Space.- 5.1 Determination of the Relevant Parameter Space.- 5.2 A Modified Minimax Estimator.- 5.3 Conditional Minimax Estimators.- 5.4 Examples.- 5.5 The Blu Property of the Modified and Conditional Minimax Estimator.- 5.6 The Modified and Conditional Estimator as Bayes Estimator.- 5.7 Sampling Designs With Constant Risk.- List of Notation.
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