The weighted likelihood

The authors consider a weighted version of the classical likelihood that applies when the need is felt to diminish the role of some of the data in order to trade bias for precision. They propose an axiomatic derivation of the weighted likelihood, for which they show that aspects of classical theory continue to obtain. They suggest a data-based method of selecting the weights and show that it leads to the James-Stein estimator in various contexts. They also provide applications. La vraisemblance pond6r6e Resume : Les auteurs considbrent une version ponddrie de la vraisemblance classique qui s'impose lorsqu'il apparait opportun d'amenuiser l'influence de certaines observations dans le but d'atteindre un 6quilibre entre biais et precision. Is ddcrivent une axiomatique qui conduit a la vraisemblance ponddrie, pour laquelle ils montrent que certains pans de la thdorie classique continuent de s'appliquer. Ils suggbrent une methode adaptative de sdlection des poids et montrent qu'elle mbne B l'estimateur de James-Stein dans diffdrents contextes. Ils presentent en outre quelques applications.

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