The $k$ nearest neighbors local linear estimator of functional conditional density when there are missing data

Abstract

Our key aim is to propose effective estimators for the conditional probability density of a scalar response variable given a functional co-variable, where the response variable is considered to have missing data at random. Such estimators are constructed by combining the approaches of the local linear method and the kernel nearest neighborhood. The main feature of this estimation is the possibility to model the missing phenomena. Under less restrictive conditions, we show the strong consistency of the proposed estimators. To assess the efficacy of the developed estimators, empirical analysis as well as real data analyses are performed.