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Asymptotic Optimal Inference for Non-ergodic Models

This monograph contains a comprehensive account of the recent work of the authors and other workers on large sample optimal inference for non-ergodic models. The non-ergodic family of models can be viewed as an extension of the usual Fisher-Rao model for asymptotics, referred to here as an ergodic f...

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Bibliographic Details
Main Authors: Basawa, I. V., Scott, D. J. (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 1983, 1983
Edition:1st ed. 1983
Series:Lecture Notes in Statistics
Subjects:
Probability Theory
Probabilities
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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
  • 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

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