A generalized reflection method of boundary correction in kernel density estimation


The kernel method of estimation of curves is now popular and widely used in statistical applications. Kernel estimators suffer from boundary effects, however, when the support of the function to be estimated has finite endpoints. Several solutions to this problem have already been proposed. Here the authors develop a new method of boundary correction for kernel density estimation. Their technique is a kind of generalized reflection involving transformed data. It generates a class of boundary corrected estimators having desirable properties such as local smoothness and nonnegativity. Simulations show that the proposed method performs quite well when compared with the existing methods for almost all shapes of densities. The authors present the theory behind this new methodology, and they determine the bias and variance of their estimators.

Canad. J. Statist.
Rohana J. Karunamuni
Rohana J. Karunamuni
Professor of Mathematics and Statistics
University of Alberta
Tom Alberts
Tom Alberts
Associate Professor of Mathematics
University of Utah