  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.
