A locally adaptive bandwidth selector for kernel based regression

Abstract

The selection of the smoothing parameter represents a crucial step in the local polynomial regression, because of the implications on the consistency of the nonparametric regression estimator and because of the difficulties in the implementation of the selection procedure. Moreover, to capture the complexity of the unknown regression curve, a local variable bandwidth is needed, which determines an increase in the efficiency and computa- tional costs of such algorithms. This paper focuses on the problem of the automatic selection of a local bandwidth. We propose a slightly different approach with respect to the traditional ones, which does not require ad- ditional computational effort. The empirical performance of the method is shown in the paper through a simulation study.