Effects of associated kernels in nonparametric multiple regressions

Associated kernels have been introduced to improve the classical continuous kernels for smoothing any function 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 a cross-validation procedure, different behaviors of multiple regression estimations are pointed out according to the type of multivariate associated kernels with correlation or not. Through simulation studies, there are no effects of correlation structures for the continuous regression functions and also for the associated continuous kernels; however, there exist real effects of the choice of multivariate associated kernels following the support of the multiple regression functions, whether bounded continuous or discrete. Applications are made on two real data sets.