Finite Sample Performance of Backfitting, Marginal Integration and Two Stage Estimators under Common Bandwidth Selection Criterion

In this paper we investigate the finite sample performance of four estimators that are currently available for additive nonparametric regression models the backfitting B-estimator, the marginal integration M-estimator and two versions of a two stage 2S-estimator, the first proposed by Kim, Linton and Hengartner (1999) and the second which we propose in this paper. We derive the conditional bias and variance of the 2S estimators and suggest a procedure to obtain optimal bandwidths that minimize an asymptotic approximation of the mean average squared error (AMASE). We are particularly concerned with the performance of these estimators when bandwidth selection is done based on data driven methods, since in this case even the asymptotic properties of the estimators are currently unavailable. We compare the estimators’ performance based on various bandwidth selection procedures currently available in the literature as well as with the procedures proposed herein via a Monte Carlo study.