Comparison of Statistical Experiments (Encyclopedia of Mathematics and its Applications)

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9780521250306: Comparison of Statistical Experiments (Encyclopedia of Mathematics and its Applications)

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.

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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.

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"The book may serve as a textbook for the mathematical background of statistics, but it is also of great importance for research. Hopefully, the monograph will inspire many statisticians to apply the methods presented also in practical problems." Arnold Janssen, Mathematical Reviews

"...impressive volume....It is very rich in content and replete with examples....quite self contained and fairly easy to read." Lucin Le Cam, SIAM Review

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