Estimation de la fonction des quantiles pour des données tronquées

Dans le modèle de troncature à gauche, deux variables aléatoires Y et T, de fonctions de répartition respectives F et G ne sont observables que si Y >= T. Considérons un échantillon observé (Yi, Ti) ; 1 = T. Let (Yi,Ti) ; 1 <= i <= n be an observed sample of this pair of random variables. The quantile function of F is estimated by the quantile function of the Lynden-Bell (1971) estimator. After giving some results of the literature in the case of independant data, we consider the a-mixing framework. We obtain strong consistency with rates, give a strong representation for the estimator of the quantile as a mean of random variables with a neglible rest and asymptotic normality. As regards the second topic of this thesis, we consider a multidimensionnal explanatory random variable X of Y which plays the role of a response. We establish strong consitency and asymptotic normality of the conditional distribution function and those of the conditional quantile function of Y given X when Y is subject to truncation. Simulations are drawn to illustrate the results for finite samples.CALAIS-BU Sciences (621932101) / SudocSudocFranceF