Contents Preface ix Part 1. Parametric Models Chapter 1. The Fisher Efficiency 3 §1.1. Statistical Experiment 3 §1.2. The Fisher Information 6 §1.3. The Cram´ er-Rao Lower Bound 7 §1.4. Efficiency of Estimators 8 Exercises 9 Chapter 2. The Bayes and Minimax Estimators 11 §2.1. Pitfalls of the Fisher Efficiency 11 §2.2. The Bayes Estimator 13 §2.3. Minimax Estimator. Connection Between Estimators 16 §2.4. Limit of the Bayes Estimator and Minimaxity 18 Exercises 19 Chapter 3. Asymptotic Minimaxity 21 §3.1. The Hodges Example 21 §3.2. Asymptotic Minimax Lower Bound 22 §3.3. Sharp Lower Bound. Normal Observations 26 §3.4. Local Asymptotic Normality (LAN) 28 §3.5. The Hellinger Distance 31 §3.6. Maximum Likelihood Estimator 33 v
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