The k-nearest neighbors estimation of the conditional mode

During the last decades, the branch of statistics dedicated to the study of functional variables has known a real development in term of theoretical developments that diversification of fields of application. We are more particularly interested in this books to the non parametric estimation of the conditional mode by the k-Nearest Neighbourd method, in which the response variable is real whereas the explanatory variable is functional (taking its values in an infinite dimensional space). The aim of this books is to study the nonparametric estimation of the conditional mode by the k-Nearest Neighbor method for functional explanatory variables. We give the rate of the almost complete convergence of the $k$-NN kernel estimator of the conditional mode. A real data application is presented to exhibit the effectiveness of this estimation method with respect to the classical kernel estimation.