Non parametric estimation of the regression operator

In this work, we are interested in the functional non parametric estimation using the k nearest neighbors method (k-NN) for a scalar response variable given a random variable taking values in a semi metric space. In the first part, we will explain how this method work (with their algorithm) by giving some concepts that help us to better understand the basic idea of the k-NN method. Then, and using these concepts, we will give the asymptotic properties for real data, vector data and functional data. In the last, we give more fields for the application of this method and giving some simulation examples to compare the kNN method and the parametric and non parametric methods.