Comparison of Statistical Experiments: 36 (Encyclopedia of Mathematics and its Applications, Series Number 36)
Cambridge University Press, 3/14/1991
EAN 9780521250306, ISBN10: 0521250307
Hardcover, 696 pages, 23.4 x 15.5 x 3.8 cm
Language: English
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.
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.