On internally corrected and symmetrized kernel estimators for nonparametric regression

We investigate the properties of a kernel-type multivariate regression estimator first proposed by Mack and Muller (Sankhya 51:59-72, 1989) in the context of univariate derivative estimation. Our proposed procedure, unlike theirs, assumes that bandwidths of the same order are used throughout; this gives more realistic asymptotics for the estimation of the function itself but makes the asymptotic distribution more complicated. We also propose a modification of this estimator that has a symmetric smoother matrix, which makes it admissible, unlike some other common regression estimators. We compare the performance of the estimators in a Monte Carlo experiment.