Boundary Problem in the Kernel Estimation of Probability Distribution Function

• Activity Number: 244
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Shunpu Zhang*+
• Companies: National Cancer Institute
• Keywords: boundary ; kernel ; distribution function

Abstract

In this paper we study the performance of the kernel distribution estimator near the ends of the support. We find that, for densities taking value zero at the endpoints, the kernel distribution estimator does not have the boundary problem and no correction is needed. However, if a density takes non-zero values at the endpoints, the kernel distribution estimator has severe boundary problem. Consequently, two methods for correcting the boundary problem of the kernel distribution estimator are proposed and their performances are compared by using numerical simulations. For the practical application of the proposed boundary corrected kernel distribution estimators, a data-dependent method for choosing the bandwidths is also proposed.