Bandwidth choice for nonparametric regression. (English) Zbl 0554.62035

Rice, John

Ann. Stat. 12, 1215-1230 (1984).

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.

Reviewer: W.J.Padgett

MSC:

62G05	Nonparametric estimation
62J02	General nonlinear regression
62G99	Nonparametric inference
62J99	Linear inference, regression

Keywords:

kernel regression estimator; tapered Fourier series estimate; unbiased estimate of mean square error; bandwidth selection; cross-validation; simulation results