kNN Estimation in Functional Partial Linear Modeling

Abstract

[Abstract]: A statistical procedure combining the local adaptivity and the easiness of implementation of k-nearest-neighbours (kNN) estimates together with the semiparametric flexibility of partial linear modeling is developed for regression problems involving functional variable. Various asymptotic results are stated, both for the linear parameters and for the nonparametric operator involved in the model. A simulation study compares the finite sample behaviour of the kNN method with alternative estimation procedures. Finally, comparison with alternative functional regression models is carried out by means of a real curves data application which exhibits the interest both of the kNN method and of the semi-parametric modeling.