The K-Nearest Neighbor Estimation of the Conditional Mode Function for Functional Data under Dependency

We focus in this paper to the estimation of the conditional mode by the k-Nearest Neighbors method (shortly k-NN).We give asymptotic results of the k-NN conditional mode estimation: the almost complete convergence and its rate under strongly mixing dependence condition. To exhibit the effectiveness of this estimation method compared to the classical kernel method estimation a real data application is given.