Certainty bands for the conditional cumulative distribution function and applications

Abstract

In this paper, we establish uniform asymptotic certainty bands for the conditional cumulative distribution function. To this aim, we give exact rate of strong uniform consistency for the local linear estimator of this function. The corollaries of this result are the asymptotic certainty bands for the quantiles and the regression function. We illustrate our results with simulations and an application on fetopathologic data.