Additive nonparametric regression estimation via back tting and marginal integration under common bandwidth selection criterion : small sample performance

Abstract

In this paper, we conducted a Monte Carlo investigation to reveal some charac- teristics of nite sample distributions of the back tting (B) and Marginal Integration (MI) estimators for an additive bivariate regression. We are particularly interested in providing some evidence on how the di¤erent methods for the selection of bandwidth, such as the plug-in method, in‡uence the nite sample properties of the MI and B estimators. We are particularly concerned with the performance of these estimators when bandwidth selection is done based in data driven methods, since in this case the aymptotics properties of these estimators are currently unavailable. The impact of ignoring the dependency between regressors is also investigated. Finally, di¤erently from what occurs at the present time, when the B and MI estimators are used ad-hoc, our objective is to provide information that allows for a more accurate comparison of these two competing alternatives in a nite sample setting.