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Comparaison de deux estimations indépendantes de la densité par la méthode de l'histogramme aléatoire. Lois limites.

Abstract : This paper deals with the problem of the comparison of two independent estimations of a density f. Given a random variable X valued on [0,1]s, with absolutely continuous d.f. F, we consider two independent samples (X1.1./i=1,n) and (X2i./i=1,n) of X, and the related estimators fn1 and fn2 of f = dF/dx, defined by the histogram method. A limit theorem is given for the extreme values of (fn1-fn2)/f n1 1/2 over [0,1]s, valid under very large conditions for f. This theorem can be used for testing the null hypothesis Pf1 = Pf2. A similar limit theorem is obtained for partial extreme values.
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Michel Béra. Comparaison de deux estimations indépendantes de la densité par la méthode de l'histogramme aléatoire. Lois limites.. Annales de l'ISUP, Publications de l’Institut de Statistique de l’Université de Paris, 1982, XXVII (1), pp.49-70. ⟨hal-03696642⟩

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