vi Contents §3.7. Proofs of Technical Lemmas 35 Exercises 40 Chapter 4. Some Irregular Statistical Experiments 43 §4.1. Irregular Models: Two Examples 43 §4.2. Criterion for Existence of the Fisher Information 44 §4.3. Asymptotically Exponential Statistical Experiment 45 §4.4. Minimax Rate of Convergence 47 §4.5. Sharp Lower Bound 47 Exercises 49 Chapter 5. Change-Point Problem 51 §5.1. Model of Normal Observations 51 §5.2. Maximum Likelihood Estimator of Change Point 54 §5.3. Minimax Limiting Constant 56 §5.4. Model of Non-Gaussian Observations 57 §5.5. Proofs of Lemmas 59 Exercises 62 Chapter 6. Sequential Estimators 65 §6.1. The Markov Stopping Time 65 §6.2. Change-Point Problem. Rate of Detection 69 §6.3. Minimax Limit in the Detection Problem. 73 §6.4. Sequential Estimation in the Autoregressive Model 75 Exercises 83 Chapter 7. Linear Parametric Regression 85 §7.1. Definitions and Notations 85 §7.2. Least-Squares Estimator 87 §7.3. Properties of the Least-Squares Estimator 89 §7.4. Asymptotic Analysis of the Least-Squares Estimator 93 Exercises 96 Part 2. Nonparametric Regression Chapter 8. Estimation in Nonparametric Regression 101 §8.1. Setup and Notations 101 §8.2. Asymptotically Minimax Rate of Convergence. Definition 103 §8.3. Linear Estimator 104
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