Comparison of Statistical Experiments [Paperback]

A comprehensive treatment of statistical experiments and an essential reference for mathematical statisticians.The present work which is devoted to the various methods of comparing statistical experiments, is essentially self-contained, requiring only some background in measure theory and functional analysis. This is a comprehensive treatment of the subject and will be an essential reference for mathematical statisticians.The present work which is devoted to the various methods of comparing statistical experiments, is essentially self-contained, requiring only some background in measure theory and functional analysis. This is a comprehensive treatment of the subject and will be an essential reference for mathematical statisticians.The present work examines the various methods of comparing statistical experiments. It begins by introducing statistical experiments and convex analysis. This chapter is followed by others on game theory, decision theory, and vector lattices, which are a natural framework for studying statistical problems. The notion of deficiency, which measures the difference in information between two experiments, is then introduced. The relation between it and other concepts, such as sufficiency, randomization, distance, ordering, equivalence, completeness and convergence are also explored. The remainder of the book is devoted to applications of the theory to linear models, local comparison of differentiable experiments, majorization, and discussions of topics complementary to the main text.Preface; Acknowledgements; 1. Statistical experiments within the measure theoretical framework; 2. Convexity; 3. Two-person, zero-sum games; 4. Statistical decision problems; 5. Vector lattices; 6. Deficiencies; 7. Equivalence, representations and functionals of experiments; 8. Comparison of linear models; 9. Majorisation and approximate majorisation; 10. Complements: Further examples, problems and comments; List of symbols; Author index; Additional references; Subl#>