  Kernel smoothers are considered near the boundary of the interval. Kernels
which minimize the expected mean square error are derived. These kernels are
equivalent to using a linear weighting function in the local polynomial
regression. It is shown that any kernel estimator that satisfies the moment
conditions up to order $m$ is equivalent to a local polynomial regression of
order $m$ with some non-negative weight function if and only if the kernel has
at most $m$ sign changes. A fast algorithm is proposed for computing the kernel
estimate in the boundary region for an arbitrary placement of data points.
