Nonparametric multiplicative distortion measurement errors models with bias reduction

Abstract

In this paper we propose a new nonparametric regression technique under multiplicative distortion measurement errors settings. The unobservable variables are both distorted in a multiplicative fashion by an observed confounding variable. A bias reduction is proposed by choosing a function that is the projection of the unknown regression function onto the parametric family in a certain metric. We find that this new technique leads to substantial improvement in the performance of regression estimators in comparison with the direct one-step estimation, irrespective of the choice of a parametric model. We obtain asymptotic normality results for the estimated nonparametric kernel smoothers, and further discuss their estimation efficiency. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators.