Effects of associated kernels in nonparametric multiple regressions

TL;DR

This paper investigates how combined associated kernels influence nonparametric multiple regression estimations, revealing that kernel choice impacts results depending on the data support type, with applications to real datasets.

Contribution

It analyzes the effects of multivariate associated kernels on regression functions, highlighting the importance of kernel selection based on data support type.

Findings

No correlation effect on continuous regression functions

Kernel choice affects estimates for bounded or discrete data

Applications demonstrate practical relevance of kernel selection

Abstract

Associated kernels have been introduced to improve the classical continuous kernels for smoothing any functional on several kinds of supports such as bounded continuous and discrete sets. This work deals with the effects of combined associated kernels on nonparametric multiple regression functions. Using the Nadaraya-Watson estimator with optimal bandwidth matrices selected by cross-validation procedure, different behaviours of multiple regression estimations are pointed out according the type of multivariate associated kernels with correlation or not. Through simulation studies, there are no effect of correlation structures for the continuous regression functions and also for the associated continuous kernels; however, there exist really effects of the choice of multivariate associated kernels following the support of the multiple regression functions bounded continuous or discrete. Applications are made on two real datasets.