Comparison of Statistical Experiments (Encyclopedia of Mathematics and its Applications, Series Number 36)

There Are A Number Of Important Questions Associated With Statistical Experiments: When Does One Given Experiment Yield More Information Than Another; How Can We Measure The Difference In Information; How Fast Does Information Accumulate By Repeating The Experiment? The Means Of Answering Such Questions Has Emerged From The Work Of Wald, Blackwell, Lecam And Others And Is Based On The Ideas Of Risk And Deficiency. 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. Chapters Introducing Statistical Experiments And The Necessary Convex Analysis Begin The Book And Are Followed By Others On Game Theory, Decision Theory And Vector Lattices. 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, Randomisation, Distance, Ordering, Equivalence, Completeness And Convergence Are Explored. This Is A Comprehensive Treatment Of The Subject And Will Be An Essential Reference For Mathematical Statisticians. Statistical Experiments Within The Measure Theoretical Framework -- Convexity -- Two-person, Zero-sum Games -- Statistical Decision Problems -- Vector Lattices -- Deficiencies -- Equivalence, Representations And Functionals Of Experiments -- Comparison Of Linear Models -- Majorization And Approximate Majorization -- Complements: Further Examples, Problems And Comments. Erik Torgersen. Includes Bibliographical References (p. [663]-664) And Indexes. 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.-- Provided by Publisher