Asymptotic normality of the k-NN single index regression estimator for functional weak dependence data*
Mustapha Mohammedi, Salim Bouzebda, Ali Laksaci, Oussama Bouanani
Abstract
In this article, we consider the k-Nearest Neighbors (k-NN) method in a single index regression model when the explanatory variable is valued in functional space in the setting of the quasi-association dependence condition. The main result of this work is the establishment of the asymptotic distribution for the k-NN kernel single index estimator. These results are established under fairly general conditions on the underlying models. As an application, the asymptotic confidence bands for the regression model based on the single-index model are presented. Some simulation studies are carried out to show the finite sample performances of the k-NN estimator.
Topics & Concepts
Asymptotic distributionEstimatorMathematicsSingle-index modelStatisticsRegression analysisKernel (algebra)Applied mathematicsKernel regressionCombinatoricsStatistical Methods and InferenceProbability and Risk ModelsBayesian Methods and Mixture Models