Asymptotic Optimal Inference for Non-ergodic Models.

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 Remarks about 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.