FDA: theoretical and practical efficiency of the local linear estimation based on the kNN smoothing of the conditional distribution when there are missing data

We aim to estimate effectively the conditional distribution function (CDF) of a scalar response variable, with missing data at random, given a functional co-variable. For this aim, we combine the local linear approach with the kernel nearest neighbours procedure to construct a new estimator of the CDF. A fundamental issue of interest is to study the impact of the missing observations on the performances of estimators. We establish, under less restrictive conditions, the strong consistency of the constructed estimator. Then, we test first its effectiveness on simulated and real datasets, and then we conclude by a comparison study with classical estimators of the CDF.