Format:
1 Online-Ressource (xx, 675 pages)
,
digital, PDF file(s)
ISBN:
9780511666353
Series Statement:
Encyclopedia of mathematics and its applications volume 36
Content:
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
Content:
Statistical experiments within the measure theoretical framework -- Convexity -- Two-person, zero-sum games -- Statistical decision problems -- Vector lattices -- Deficiencies -- Equivalence, representations and functionals of experiments -- Comparison of linear models -- Majorization and approximate majorization -- Complements: further examples, problems and comments
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9780521250306
Additional Edition:
ISBN 9780521102827
Additional Edition:
Erscheint auch als Druckausgabe Torgersen, Erik Comparison of statistical experiments Cambridge [u.a.] : Cambridge Univ. Press, 1991 ISBN 0521250307
Language:
English
Subjects:
Mathematics
Keywords:
Statistische Entscheidungstheorie
DOI:
10.1017/CBO9780511666353
