Comparison of Statistical Experiments
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Part of Encyclopedia of Mathematics and its Applications
- Author: Erik Torgersen, Universitetet i Oslo
- Date Published: March 2009
- availability: Available
- format: Paperback
- isbn: 9780521102827
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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.
Reviews & endorsements
"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
See more 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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×Product details
- Date Published: March 2009
- format: Paperback
- isbn: 9780521102827
- length: 696 pages
- dimensions: 234 x 156 x 37 mm
- weight: 0.96kg
- availability: Available
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.
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