Theory of Statistical Experiments - H. Heyer

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Sommaire:
I. Games and Statistical Decisions.- ? 1. Two-Person Zero Sum Games.- ? 2. Concave-Convex Games and Optimality.- ? 3. Basic Principles of Statistical Decision Theory.- II. Sufficient ?-Algebras and Statistics.- ? 4. Generalities.- ? 5. Properties of the System of All Sufficient ?-Algebras.- ? 6. Completeness and Minimal Sufficiency.- III. Sufficiency under Additional Assumptions.- ? 7. Sufficiency in the Separable Case.- ? 8. Sufficiency in the Dominated Case.- ? 9. Examples and Counter-Examples.- IV. Testing Experiments.- ?10. Fundamentals.- ?11. Construction of Most Powerful Tests.- ?12. Least Favorable Distributions and Bayes Tests.- V. Testing Experiments Admitting an Isotone Likelihood Quotient.- ?13. Isotone Likelihood Quotient.- ?14. One-Dimensional Exponential Experiments.- ?15. Similarity, Stringency and Unbiasedness.- VI. Estimation Experiments.- ?16. Minimum Variance Unbiased Estimators.- ?17. p-Minimality.- ?18. Estimation Via the Order Statistic.- VII. Information and Sufficiency.- ?19. Comparison of Classical Experiments.- ?20. Representation of Positive Linear Operators by Stochastic Kernels.- ?21. The Stochastic Kernel Criterion.- ?22. Sufficiency in the Sense of Blackwell.- VIII. Invariance and the Comparison of Experiments.- ?23. Existence of Invariant Stochastic Kernels.- ?24. Comparison of Translation Experiments.- ?25. Comparison of Linear Normal Experiments.- IX. Comparison of Finite Experiments.- ?26. Comparison by k-Decision Problems.- ?27. Comparison by Testing Problems.- ?28. Standard Experiments.- ?29. General Theory of Standard Measures.- ?30. Sufficiency and Completeness.- X. Comparison with Extremely Informative Experiments.- ?31. Bayesian Deficiency.- ?32. Totally Informative Experiments.- ?33. TotallyUninformative Experiments.- ?34. Inequalities Between Deficiencies.- Notational Conventions.- References.- Symbol Index.