Theory of Statistical Experiments

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. Language: English