  This article examines density estimation by combining a parametric approach
with a nonparametric factor. The plug-in parametric estimator is seen as a
crude estimator of the true density and is adjusted by a nonparametric factor.
The nonparametric factor is derived by a criterion called local
  L_2-fitting. A class of estimators that have multiplicative adjustment is
provided, including estimators proposed by several authors as special cases,
and the asymptotic theories are developed. Theoretical comparison reveals that
the estimators in this class are better than, or at least competitive with, the
traditional kernel estimator in a broad class of densities. The asymptotically
best estimator in this class can be obtained from the elegant feature of the
bias function.
