Multiplicative Bias Corrected Nonparametric Smoothers

TL;DR

This paper introduces a multiplicative bias correction method for nonparametric regression estimators, achieving zero asymptotic bias and maintaining variance, with practical effectiveness demonstrated through simulations.

Contribution

It provides a new bias correction technique that improves nonparametric smoothers by reducing bias without increasing variance, supported by asymptotic analysis.

Findings

Zero asymptotic bias achieved

Variance remains comparable to local linear estimators

Effective for modest sample sizes in simulations

Abstract

The paper presents a multiplicative bias reduction estimator for nonparametric regression. The approach consists to apply a multiplicative bias correction to an oversmooth pilot estimator. In Burr et al. [2010], this method has been tested to estimate energy spectra. For such data set, it was observed that the method allows to decrease bias with negligible increase in variance. In this paper, we study the asymptotic properties of the resulting estimate and prove that this estimate has zero asymptotic bias and the same asymptotic variance as the local linear estimate. Simulations show that our asymptotic results are available for modest sample sizes.