Convergence presque sûre de l'estimateur linéaire local de la fonction de répartition conditionnelle

Abstract

The local linear estimator of the conditional cumulative distribution function is shown to be the ratio of two U-statistics. Using results from the theory of U-statistics, we show the almost sure convergence of this estimator both locally and globally. This is used to establish the almost sure convergence of conditional quantiles computed from the linear estimator.