Neyman Factorization and Minimality of Pairwise Sufficient Subfields

Ghosh, Joyee; Morimoto, Haruki; Yamada, Sakutarō

doi:10.1214/aos/1176345456

Cited by 11 publications

(6 citation statements)

References 8 publications

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“…Nevertheless, as shown in [2], minimal sufficient σ-fields exist and the Neyman factorization theorem holds good. These results were extended for pairwise sufficient σ-fields and condition for existence of minimal pairwise sufficient σ-field was found in [37].…”

Section: Foundations Of Statisticsmentioning

confidence: 88%

J. K. Ghosh’s contribution to statistics: A brief outline

Clarke¹,

Ghosal²

2008

Institute of Mathematical Statistics Collections

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Professor Jayanta Kumar Ghosh has contributed massively to various areas of Statistics over the last five decades. Here, we survey some of his most important contributions. In roughly chronological order, we discuss his major results in the areas of sequential analysis, foundations, asymptotics, and Bayesian inference. It is seen that he progressed from thinking about data points, to thinking about data summarization, to the limiting cases of data summarization in as they relate to parameter estimation, and then to more general aspects of modeling including prior and model selection.

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Section: Foundations Of Statisticsmentioning

confidence: 88%

J. K. Ghosh’s contribution to statistics: A brief outline

Clarke¹,

Ghosal²

2008

Institute of Mathematical Statistics Collections

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“…From the definition of /~ (proof of Proposition 2.3) it is clear that it can be extended to a measure /~ on ~ and that (~, ~,/~) is strictly localizable (Fremlin [3], p. 17.2, a direct sum of finite measure spaces). Experiments majorized by a localizable measure retain several properties of experiments dominated by a finite measure (see for example, Ghosh et al [4] and the references given there).…”

Section: Introductionmentioning

confidence: 98%

On a characterization of monotone likelihood ratio experiments

Mussmann

1987

Ann Inst Stat Math

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SummaryPfanzagl (1962, Zeit. Wahrscheinlichkeitsth., 1, 109-115) showed that a dominated family of probability measures has monotone likelihood ratios with respect to some real valued statistic if there exists a set of tests which has certain nice properties. A similar characterization was given by Dettweiler (1978, Metrika, 25, 247-254), who did not assume domination. However, Pfanzagl's result is not a special case of the one proved by Dettweiler. We present a theorem which comprises the results of both authors. Our proof shows that not all conditions introduced by them are needed. Furthermore, we investigate the question concerning the generality we get if we do not assume domination.

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“…Savage [8], R. R. Bahadur [1], D. L. Burkholder [5], R. A. Fisher [6] and L. Le Cam [10]. Sufficiency can be characterized by a factorization criterion, and by means of this criterion a minimal sufficient subfield can be constructed ( [2], [3], [7]). …”

Section: Introductionmentioning

confidence: 99%