Author | Basawa, Ishwar V. author |
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Title | Asymptotic Optimal Inference for Non-ergodic Models [electronic resource] / by Ishwar V. Basawa, David John Scott |
Imprint | New York, NY : Springer New York, 1983 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5505-5 |
Descript | XIII, 170 p. online resource |
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 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