A modified version of a kernel regression estimator is analyzed with respect to choice of bandwidth. The modification consists of replacing the kernel estimate by a tapered Fourier series estimate which simplifies some technical arguments.
It is shown that the bandwidth chosen based on an unbiased estimate of mean square error is asymptotically optimal. Several other methods of bandwidth selection, including cross-validation, are examined and shown to be asymptotically equivalent. However, some simulation results indicate that for small or moderate sample sizes the methods are quite different.