Asymptotic Optimal Inference for Non-ergodic Models

0. An Over-view. - 1. Introduction. - 2. The Classical Fisher-Rao Model for Asymptotic Inference. - 3. Generalisation of the Fisher-Rao Model to Non-ergodic Type Processes. - 4. Mixture Experiments and Conditional Inference. - 5. Non-local Results. - 1. A General Model and Its Local Approximation. - 1. Introduction. - 2. LAMN Families. - 3. Consequences of the LAMN Condition. - 4. Sufficient Conditions for the LAMN Property. - 5. Asymptotic Sufficiency. - 6. An Example (Galton-Watson Branching Process). - 7. Bibliographical Notes. - 2. Efficiency of Estimation. - 1. Introduction. - 2. Asymptotic Structure of Limit Distributions of Sequences of Estimators. - 3. An Upper Bound for the Concentration. - 4. The Existence and Optimality of the Maximum Likelihood Estimators. - 5. Optimality of Bayes Estimators. - 6. Bibliographical Notes. - 3. Optimal Asymptotic Tests. - 1. Introduction. - 2. The Optimality Criteria: Definitions. - 3. An Efficient Test of Simple Hypotheses: Contiguous Alternatives. - 4. Local Efficiency and Asymptotic Power of the Score Statistic. - 5. Asymptotic Power of the Likelihood Ratio Test: Simple Hypothesis. - 6. Asymptotic Powers of the Score and LR Statistics for Composite Hypotheses with Nuisance Parameters. - 7. An Efficient Test of Composite Hypotheses with Contiguous Alternatives. - 8. Examples. - 9. Bibliographical Notes. - 4. Mixture Experiments and Conditional Inference. - 1. Introduction. - 2. Mixture of Exponential Families. - 3. Some Examples. - 4. Efficient Conditional Tests with Reference to L. - 5. Efficient Conditional Tests with Reference to L?. - 6. Efficient Conditional Tests with Reference to LC: Bahadur Efficiency. - 7. Efficiency of Conditional Maximum Likelihood Estimators. - 8. Conditional Tests for Markov Sequences and Their Mixtures. - 9. Some Heuristic Remarksabout Conditional Inference for the General Model. - 10. Bibliographical Notes. - 5. Some Non-local Results. - 1. Introduction. - 2. Non-local Behaviour of the Likelihood Ratio. - 3. Examples. - 4. Non-local Efficiency Results for Simple Likelihood Ratio Tests. - 5. Bibiographical Notes. - Appendices. - A. 1 Uniform and Continuous Convergence. - A. 2 Contiguity of Probability Measures. - References. Language: English