ASYMPTOTIC PROPERTIES OF A CONDITIONAL RISK FUNCTION FOR FUNCTIONAL DATA

In this paper, we investigate the asymptotic normality of the kernel density estimator (introduced by Ferraty and Vieu (2000)) under dependent conditions of the conditional hazard function, The infill increasing setting is considered, that is when the covariates take values in some abstract function space. Our approach is based on the Doob’s technique. It is shown that, under the concentration property on small balls of the probability measure of the functional estimator and some regularity conditions, the kernel estimate of the three parameters (conditional density, conditional distribution and conditional hazard) are asymptotically normally distributed.