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.
Publié le : 1997-07-05
Classification:
théorie de la décision,
test,
Neyman-Pearson,
Bol'shev,
hypothèses unilatérales et bilatérales,
p-value,
distribution a posteriori,
rapport de vraisemblance monotone,
modèle exponentiel,
62A, 62C, 62f, 62P,
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
@article{hal-00019718,
author = {Morel, Guy},
title = {Expertises : proc\'edures statistiques d'aide \`a la d\'ecision},
journal = {HAL},
volume = {1997},
number = {0},
year = {1997},
language = {fr},
url = {http://dml.mathdoc.fr/item/hal-00019718}
}
Morel, Guy. Expertises : procédures statistiques d'aide à la décision. HAL, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/hal-00019718/