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.