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Erschienen in:
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2017 | OriginalPaper | Buchkapitel

2. Sufficiency

verfasst von : Johann Pfanzagl

Erschienen in: Mathematical Statistics

Verlag: Springer Berlin Heidelberg

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Abstract

This essay describes the historical development of the concepts of exhaustive statistics and of sufficiency of statistics and sub-\(\sigma \)-fields. We discuss the relations between these concepts, Neyman’s factorization theorem, completeness and bounded completeness of families of distributions, completeness of exponential families, minimal sufficiency, trivial sufficiency, and different characterizations of sufficiency: decision theoretic, by power of tests, by concentration of unbiased estimators, and by measures of information.

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Vorheriges Kapitel Introduction
Nächstes Kapitel Descriptive Statistics
Fußnoten
1
It is interesting to observe how the authorship of a nontrivial example was lost as time went on. Dieudonné’s example appears in various textbooks as an exercise with reference to the author (e.g. Doob 1953, p. 624; Halmos 1950, p. 210, Exercise 4 and p. 292, Reference to Sect. 48; Dudley 1989, p. 275, Problem 6 and Note Sect. 10.2, p. 298). It also appears in Ash 1972, p. 267, Problem 4, without reference to Dieudonné, and in Romano and Siegel (1986), pp. 138/9, Example 6.13, as an “Example given in Ash”. In Lehmann and Casella (1998, p. 35) it was presented as an “Example due to Ash, presented by Romano and Siegel (1986)”.
 
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Metadaten
Titel
Sufficiency
verfasst von
Johann Pfanzagl
Copyright-Jahr
2017
Verlag
Springer Berlin Heidelberg
Buch
Mathematical Statistics

Print ISBN: 978-3-642-31083-6

Electronic ISBN: 978-3-642-31084-3

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-642-31084-3_2