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Un estimateur non paramétrique de la moyenne d’un sous-groupe : le para-bootstrap studentisé

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Introduction : Pour une variable aléatoire suivant une loi asymétrique sur un très petit échantillon (n<10), aucune méthode classique ne permet l'estimation d'un intervalle de confiance de la moyenne. La méthode de Student, comme le bootstrap non paramétrique sont trop biaisés et le bootstrap paramétrique est impossible lorsque la famille de lois est inconnue. Objectif : Estimer un intervalle de confiance sur un très petit échantillon (n entre 5 et 20) lorsque celui-ci est un sous-groupe d'un plus grand échantillon (n>=30). Méthodes : Ce travail repose sur l'hypothèse d'égalité de la forme (moments d'ordre >= 3) de la distribution entre le sous-groupe et le reste du grand échantillon, sans forcément égalité des moyennes ou variances. Il s'agit d'une variante du bootstrap studentisé. Les deux sous-groupes (petit et grand) sont chacun centrés et réduits, puis réunis. Les échantillons de bootstrap sont tirés au sort avec remise dans cette échantillon centré réduit réuni. Cette méthode novatrice a été nommée : "Le para-bootstrap studentisé".
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