Variable bandwidth in nonparametric regression^∗

^∗This research was supported by S. N. U. Research Fund, 1997.

Abstract

In the context of estimating a probability density function use of a suitable variable bandwidth is known to improve the rate of convergence of the resulting kernel density estimator. In this paper we show that the same kind of improvement is possible in the regression setting. In particular we find that the fast rate of convergence derived by Hall (1990), using a bandwidth variation method that depends on the underlying regression function still holds when one uses an estimate of the regression function as a pilot.

Keywords:

• Kernel smoothing
• regression function
• internal estimator
• rate of convergence
• asymptotic distribution

^∗This research was supported by S. N. U. Research Fund, 1997.

^†Corresponding author.

^∗This research was supported by S. N. U. Research Fund, 1997.

^†Corresponding author.

Notes

^∗This research was supported by S. N. U. Research Fund, 1997.

^†Corresponding author.