Comparison of Statistical Experiments

by Erik Torgersen

Overview

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.

Product Details

ISBN-13:	9780521102827
Publisher:	Cambridge University Press
Publication date:	03/12/2009
Series:	Encyclopedia of Mathematics and its Applications , #36
Pages:	696
Product dimensions:	6.14(w) x 9.21(h) x 1.46(d)

Table of Contents

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; Subject index.

Editorial Reviews

"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

From the Publisher