A Locally Adaptive Method of Boundary Correction in Kernel Density Estimation
by
R.J. Karunamuni
University of Alberta

Kernel smoothing methods are widely used in many research areas of statistics. However, kernel methods suffer from boundary effects when the support of the function to be estimated has finite endpoints. Boundary effects seriously affect the overall performance of the estimator. In this article, we propose a new method of boundary correction for univariate kernel density estimation. Our technique is based on a data transformation that depends on the point of estimation. The proposed method possesses desirable properties such as the local adaptivity and non-negativity of the proposed estimator. Furthermore, unlike other transformation methods available, the estimator is easy to implement. In a Monte Carlo study, the performance of the proposed estimator is numerically analyzed and compared with the existing methods of boundary correction. The theory behind the new methodology along with the bias and variance of the proposed estimator are presented.

Date received: August 27, 2003