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.