Minimax Solutions in Sampling from Finite Populations

Inhaltsverzeichnis

• 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.