Empirical-Bias Bandwidths for Spatial Local Polynomial Regression with Correlated Errors

Torgny Lindström

Abstract:: The empirical-bias bandwidth selector (EBBS) is a method for data-driven selection of bandwidths for local polynomial regression. It is a bandwidth selection method for estimation of the mean-function and its partial derivatives of any order as well as for estimation of the variance-function. Moreover EBBS allows for univariate as well as multivariate; predictor variables.
: In this paper we introduce the empirical-bias bandwidth selector, EBBS_dep. This estimation procedure is adjusted to allow for dependent errors and selection of diagonal or full bandwidth matrices for estimation of the mean-function or one of its partial derivatives as well as for estimation of the variance-function. Asymptotic results for the conditional bias of the first order partial derivative; estimates are given for the local quadratic regression case.
: A simulation study is performed to compare the adjusted and the original version of EBBS with theoretical results for a few cases displaying varying degrees of positive correlation.

Key words:: Derivative estimation; heteroscedasticity; local bandwidth selection; surface fitting; variance-function estimation.