Springer Statistics

I. Games and Statistical Decisions.- x 1. Two-Person Zero Sum Games.- x 2. Concave-Convex Games and Optimality.- x 3. Basic Principles of Statistical Decision Theory.- II. Sufficient ?-Algebras and Statistics.- x 4. Generalities.- x 5. Properties of the System of All Sufficient ?-Algebras.- x 6. Completeness and Minimal Sufficiency.- III. Sufficiency under Additional Assumptions.- x 7. Sufficiency in the Separable Case.- x 8. Sufficiency in the Dominated Case.- x 9. Examples and Counter-Examples.- IV. Testing Experiments.- x10. Fundamentals.- x11. Construction of Most Powerful Tests.- x12. Least Favorable Distributions and Bayes Tests.- V. Testing Experiments Admitting an Isotone Likelihood Quotient.- x13. Isotone Likelihood Quotient.- x14. One-Dimensional Exponential Experiments.- x15. Similarity, Stringency and Unbiasedness.- VI. Estimation Experiments.- x16. Minimum Variance Unbiased Estimators.- x17. p-Minimality.- x18. Estimation Via the Order Statistic.- VII. Information and Sufficiency.- x19. Comparison of Classical Experiments.- x20. Representation of Positive Linear Operators by Stochastic Kernels.- x21. The Stochastic Kernel Criterion.- x22. Sufficiency in the Sense of Blackwell.- VIII. Invariance and the Comparison of Experiments.- x23. Existence of Invariant Stochastic Kernels.- x24. Comparison of Translation Experiments.- x25. Comparison of Linear Normal Experiments.- IX. Comparison of Finite Experiments.- x26. Comparison by k-Decision Problems.- x27. Comparison by Testing Problems.- x28. Standard Experiments.- x29. General Theory of Standard Measures.- x30. Sufficiency and Completeness.- X. Comparison with Extremely Informative Experiments.- x31. Bayesian Deficiency.- x32. Totally Informative Experiments.- x33. Totally Uninformative Experiments.- x34. Inequalities Between Deficiencies.- Notational Conventions.- References.- Symbol Index.