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arXiv: math.ST/0602611

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Expertises : procédures statistiques d'aide à la décision (1997) 175

Expertises : procédures statistiques d'aide à la décision

Guy Morel 1, 2

(1997)

In this study, we introduce a new approach to statistical decision theory. Without using a loss function, we select good decision rules to choice between two hypotheses. We call them "experts". They are globally unbiased but also conditionally unbiased on a family of events. We do not try to define the best expert. We define a probability distribution on the space of "experts". The measure of evidence for a hypothesis is the inductive probability of experts that decide this hypothesis, we call this measure: a "vote". We compare this point of view with the p-values. For some family of hypotheses, the "votes" can define a probability on the space of parameters. We compare these results with the Bayes posterior distributions. We study in detail real-parameter families of distributions with monotone likelihood ratio and multiparameter exponential families.

1:	Laboratoire de Mathématiques et Physique Théorique (LMPT)
	CNRS : UMR6083 – Université François Rabelais - Tours
2:	Cités, Territoires, Environnement et Sociétés (CITERES)
	CNRS : UMR6173 – Université François Rabelais - Tours

Subject

:

Mathematics/Statistics

Keyword(s): théorie de la décision – test – Neyman-Pearson – Bol'shev – hypothèses unilatérales et bilatérales – p-value – distribution a posteriori – rapport de vraisemblance monotone – modèle exponentiel

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From: Guy Morel <>

Submitted on: Monday, 27 February 2006 10:28:08

Updated on: Monday, 27 February 2006 10:53:42