Local linear estimation of the conditional mode under left truncation for functional regressors

Abstract

In this work, we introduce a local linear estimator of the conditional mode for a random real response variable which is subject to left-truncation by another random variable where the covariate takes values in an infinite dimensional space. We first establish both of pointwise and uniform almost sure convergences, with rates, of the conditional density estimator. Then, we deduce the strong consistency of the obtained conditional mode estimator. We finally illustrate the outperformance of our method with respect to the kernel one through a simulation study for a finite sample with different rates of truncation and sizes.