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

Torgersen, Erik

Softcover

ISBN 10: 0521102820 ISBN 13: 9780521102827

Publisher: Cambridge University Press, 2009

Synopsis

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.

About this title

Review

"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

Book Description

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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2009
• Language: English
• ISBN 10: 0521102820
• ISBN 13: 9780521102827
• Binding: Paperback
• Edition number: 1
• Number of pages: 696