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Statistical Information and Likelihood


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Table of Contents

I Information and Likelihood.- I Recovery of Ancillary Information.- 0. Notes.- 1. Introduction.- 2. The Sample Size Analogy.- 3. A Logical Difficulty.- 4. Conceptual Statistical Experiments.- II Statistical Information and Likelihood Part I: Principles.- 0. Notes.- 1. Statistical Information.- 2. Basic Definitions and Relations.- 3. Some Principles of Inference.- 4. Information as a Function.- 5. Fisher Information.- 6. The Likelihood Principle.- III Statistical Information and Likelihood Part II: Methods.- 0. Notes.- 1. Non-Bayesian Likelihood Methods.- 2. Likelihood: Point Function or a Measure ?.- 3. Maximum Likelihood.- IV Statistical Information and Likelihood Part III: Paradoxes.- 0. Notes.- 1. A Fallacy of Five Terms.- 2. The Stopping Rule Paradox.- 3. The Stein Paradox.- V Statistical Information and Likelihood: Discussions.- 0. Notes.- 1. Discussions.- 2. Barnard-Basu Correspondence.- VI Partial Sufficiency.- 0. Notes.- 1. Introduction.- 2. Specific Sufficient Statistics.- 3. Partial Sufficiency.- 4. H-sufficiency.- 5. Invariantly Sufficient Statistics.- 6. Final Remarks.- VII Elimination of Nuisance Parameters.- 0. Notes.- 1. The Elimination Problem and Methods.- 2. Marginalization and Conditioning.- 3. Partial Sufficiency and Partial Ancillarity.- 4. Generalized Sufficiency and Conditionality Principles.- 5. A Choice Dilemma.- 6. A Conflict.- 7. Rao-Blackwell Type Theorems.- 8. The Bayesian Way.- 9. Unrelated Parameters.- VIII Sufficiency and Invariance.- 0. Notes.- 1. Summary.- 2. Definitions and Preliminaries.- 3. A Mathematical Introduction.- 4. Statistical Motivation.- 5. When a Boundedly Complete Sufficient Sub-field Exists.- 6. The Dominated Case.- 7. Examples.- 8. Transformations of a Set of Normal Variables.- 9. Parameter-preserving Transformations.- 10. Some Typical Invariance Reductions.- 11. Some Final Remarks.- IX Ancillary Statistics, Pivotal Quantities and Confidence.- Statements.- 1. Introduction.- 2. Ancillary Statistics.- 3. Ancillary Information.- 4. Pivotal Quantities.- 5. Confidence Statements.- 6. Ancillarity in Survey Sampling.- II Survey Sampling and Randomization.- X Sufficiency in Survey Sampling.- 1. Introduction and Summary.- 2. Sufficient Statistics and Sub-Fields.- 3. Pitcher and Burkholder Pathologies.- 4. Sufficiency in Typical Sampling Situations.- XI Likelihood Principle and Survey Sampling.- 0. Notes.- 1. Introduction.- 2. Statistical Models and Sufficiency.- 3. Sufficiency in Discrete Models.- 4. The Sample Survey Models.- 5. The Sufficiency and Likelihood Principles.- 6. Role and Choice of the Sampling Plan.- 7. Concluding Remarks.- XII On the Logical Foundations of Survey Sampling.- 1. An Idealization of the Survey Set-up.- 2. Probability in Survey Theory.- 3. Non-sequential Sampling Plans and Unbiased Estimation.- 4. The Label-set and the Sample Core.- 5. Linear Estimation in Survey Sampling.- 6. Homogeneity, Necessary Bestness and Hyper-Admissibility.- 7. Linear Invariance.- XIII On the Logical Foundations of Survey Sampling: Discussions.- 1. Discussions.- 2. Author’s Reply.- XIV Relevance of Randomization in Data Analysis.- 0. Notes.- 1. Introduction.- 2. Likelihood.- 3. A Survey Sampling Model.- 4. Why Randomize?.- 5. Randomization Analysis of Data.- 6. Randomization and Information.- 7. Information in Data.- 8. A Critical Review.- XV The Fisher Randomization Test.- 0. Notes.- 1. Introduction.- 2. Randomization.- 3. Two Fisher Principles.- 4. The Fisher Randomization Test.- 5. Did Fisher Change His Mind?.- 6. Randomization and Paired Comparisons.- 7. Concluding Remarks.- XVI The Fisher Randomization Test: Discussions.- 1. Discussions.- 2. Rejoinder.- III Miscellaneous Notes and Discussions.- XVII Likelihood and Partial Likelihood.- XVIII A Discussion on the Fisher Exact Test.- XIX A Discussion on Survey Theory.- XX A Note on Unbiased Estimation.- XXI The Concept of Asymptotic Efficiency.- XXII Statistics Independent of a Complete Sufficient Statistic.- XXIII Statistics Independent of a Sufficient Statistic.- XXIV The Basu Theorems.- References.

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