Some asymptotic results of a k NN conditional mode estimator for functional stationary ergodic data

This article investigates the conditional mode estimation of a univariate response variable given a functional random covariate (i.e., valued in some infinite-dimensional space) whenever a stationary ergodic data are considered. We construct a new estimator of the conditional mode which is constructed by a kNN approach. Under less restrictive conditions, we show the strong consistency of the proposed estimator. To assess the efficiency of the developed estimator, empirical analysis as well as real data analyses are performed.