  In this paper, we investigate the theoretical and empirical properties of
$L_2$ boosting with kernel regression estimates as weak learners. We show that
each step of $L_2$ boosting reduces the bias of the estimate by two orders of
magnitude, while it does not deteriorate the order of the variance. We
illustrate the theoretical findings by some simulated examples. Also, we
demonstrate that $L_2$ boosting is superior to the use of higher-order kernels,
which is a well-known method of reducing the bias of the kernel estimate.
