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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