Comparison of statistical experiments / Erik Torgersen.Material type: TextSeries: Encyclopedia of mathematics and its applications: v. 36.Publisher: Cambridge ; New York : Cambridge University Press, 1991Description: 1 online resource (xx, 675 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9781107087224; 1107087228; 9780511666353; 0511666357Subject(s): Statistical decision | Mathematical statistics | Prise de décision (Statistique) | Statistique mathématique | MATHEMATICS -- Probability & Statistics -- Bayesian Analysis | Mathematical statistics | Statistical decision | Statistiek | Besliskunde | Experimenten | Décision, prise de (Statistique) | Statistique mathématiqueGenre/Form: Electronic books. | Electronic books. Additional physical formats: Print version:: Comparison of statistical experiments.DDC classification: 519.5/42 LOC classification: QA279.4Other classification: 31.73 | *62B15 | 62-02 | 62B05 | 62C05 Online resources: Click here to access online
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Includes bibliographical references (pages 663-664) and indexes.
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.
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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.