Confidence Distribution, the Frequentist Distribution Estimator of a Parameter: A Review

Il est courant, en inférence fréquentielle, d'utiliser un point unique (une estimation ponctuelle) ou un intervalle (intervalle de confiance) dans le but d'estimer un paramètre d'intér^t. Une question très simple se pose: peut‐on également utiliser, dans le même but, et dans la même optique fréquentielle, à la façon dont les Bayésiens utilisent une loi a posteriori, une distribution de probabilité? La réponse est affirmative, et les distributions de confiance apparaissent comme un choix naturel dans ce contexte. Le concept de distribution de confiance a une longue histoire, longtemps associée, à tort, aux théories d'inférence fiducielle, ce qui a compromis son développement dans l'optique fréquentielle. Les distributions de confiance ont récemment attiré un regain d'intérêt, et plusieurs résultats ont mis en évidence leur potentiel considérable en tant qu'outil inférentiel. Cet article présente une définition moderne du concept, et examine les ses évolutions récentes. Il aborde les méthodes d'inférence, les problèmes d'optimalité, et les applications. A la lumière de ces nouveaux développements, le concept de distribution de confiance englobe et unifie un large éventail de cas particuliers, depuis les exemples paramétriques réguliers (distributions fiducielles), les lois de rééchantillonnage, les p‐valeurs et les fonctions de vraisemblance normalisées jusqu'aux a priori et posteriori bayésiens. La discussion est entièrement menée d'un point de vue fréquentiel, et met l'accent sur les applications dans lesquelles les solutions fréquentielles sont inexistantes ou d'une application difficile. Bien que nous attirions également l'attention sur les similitudes et les différences que présentent les approches fréquentielle, fiducielle, et Bayésienne, notre intention n'est pas de rouvrir un débat philosophique qui dure depuis près de deux cents ans. Nous espérons bien au contraire contribuer à combler le fossé qui existe entre les différents points de vue.

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