Minimax Solutions in Sampling from Finite Populations

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. Language: English