Pitman's Measure of Closeness: A Comparison of Statistical Estimators.

原文摘要

Preface Part I. Introduction 1. Evolution of Estimation Theory Least Squares Method of Moments Maximum Likelihood Uniformly Minimum Variance Unbiased Estimation Biased Estimation Bayes and Empirical Bayes Influence Functions and Resampling Techniques Future Directions 2. PMC Comes of Age PMC: A Product of Controversy PMC as an Intuitive Criterion 3. The Scope of the Book History, Motivation, and Controversy of PMC A Unified Development of PMC Part II. Development of Pitman's Measure of Closeness: 1. The Intrinsic Appeal of PMC Use of MSE Historical Development of PMC Convenience Store Example 2. The Concept of Risk Renyi's Decomposition of Risk How Do We Understand Risk? 3. Weakness in the Use of Risk When MSE Does Not Exist Sensitivity to the Choice of the Loss Function The Golden Standard 4. Joint Versus Marginal Information Comparing Estimators with an Absolute Ideal Comparing Estimators with One Another 5. Concordance of PMC with MSE and MAD Part III. Anomalies with PMC: 1. Living in an Intransitive World Round-Robin Competition Voting Preferences Transitiveness 2. Paradoxes Among Choice The Pairwise-Worst Simultaneous-Best Paradox The Pairwise-Best Simultaneous-Worst Paradox Politics: The Choice of Extremes 3. Rao's Phenomenom 4. The Question of Ties Equal Probability of Ties Correcting the Pitman Criterion A Randomized Estimator 5. The Rao-Berkson Controversy Minimum Chi-Square and Maximum Likelihood Model Inconsistency Remarks Part 4. Pairwise Comparisons 1. Geary-Rao Theorem 2. Applications of the Geary-Rao Theorem 3. Karlin's Corollary 4. A Special Case of the Geary-Rao Theorem Surjective Estimators The MLR Property 5. Applications of the Special Case 6. Transitiveness Transitiveness Theorem Another Extension of Karlin's Corollary Part V. Pitman-Closest Estimators: 1. Estimation of Location Parameters 2. Estimators of Scale 3. Generalization via Topological Groups 4. Posterior Pitman Closeness 5. Linear Combinations 6. Estimation by Order Statistics Part 6. Asymptotics and PMC 1. Pitman Closeness of BAN Estimators Modes of Convergence Fisher Information BAN Estimates are Pitman Closet 2. PMC by Asymptotic Representations A General Proposition 3. Robust Estimation of a Location Parameter L-Estimators M-Estimators R-Estimators 4. APC Characterizations of Other Estimators Pitman Estimators Examples of Pitman Estimators PMC Equivalence Bayes Estimators 5. Second-Order Efficiency and PMC Asymptotic Efficiencies Asymptotic Median Unbiasedness Higher-Order PMC Index Bibliography.

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