AISM 54, 312-323

© 2002 ISM

## Local linear smoothers using asymmetric kernels

### Song Xi Chen

Department of Statistics and Applied Probability,
National University of Singapore, Singapore 117543, Singapore, e-mail: stacsx@nus.edu.sg

(Received January 4, 2000; revised January 16, 2001)

Abstract.
This paper considers using asymmetric kernels in local linear smoothing
to estimate a regression curve with bounded support. The asymmetric kernels are
either beta kernels if the curve has a compact support or gamma kernels if the
curve is bounded from one end only. While possessing the standard benefits of
local linear smoothing, the local linear smoother using the beta or gamma kernels
offers some extra advantages in aspects of having finite variance and
resistance to sparse design. These are due to their flexible kernel shape and the
support of the kernel matching the support of the regression curve.

Key words and phrases:
Beta kernels, gamma kernels, local linear smoother, nonparametric regression, sparse region.

**Source**
(TeX , DVI )