  A variance reduction technique in nonparametric smoothing is proposed: at
each point of estimation, form a linear combination of a preliminary estimator
evaluated at nearby points with the coefficients specified so that the
asymptotic bias remains unchanged. The nearby points are chosen to maximize the
variance reduction. We study in detail the case of univariate local linear
regression. While the new estimator retains many advantages of the local linear
estimator, it has appealing asymptotic relative efficiencies. Bandwidth
selection rules are available by a simple constant factor adjustment of those
for local linear estimation. A simulation study indicates that the finite
sample relative efficiency often matches the asymptotic relative efficiency for
moderate sample sizes. This technique is very general and has a wide range of
applications.
