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On internally corrected and symmetrized kernel estimators for nonparametric regression | David Jacho-Chavez

On internally corrected and symmetrized kernel estimators for nonparametric regression

Abstract

We investigate the properties of a kernel-type multivariate regression estimator first proposed by Mack and Müller (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.

Publication
Test, (19), 1, pp. 166-186, https://doi.org/10.1007/s11749-009-0145-y