Boundary Kernels

Exact Boundary Kernels for Density Estimation on a Compact Support with Boundary Conditions
Jungmo Yoon

We develop a method to obtain exact kernel functions for a density estimation problem in which the density function is defined on a finite domain with boundary conditions. If economic theories require certain conditions to be satisfied at the boundary of domain, our method provides a way to incorporate the information contained in boundary conditions in the kernel density estimators. We extend the literature dealing with a one-sided boundary in one dimensional problem to a finite domain such as a two-sided interval. Our approach can be extended to a multi-dimensional problem in a natural way. Our method provides the exact kernel function, that is, it satisfies the boundary conditions not only in an asymptotic sense but also in small samples.

The paper is available upon request.