Exact Boundary Correction Methods for Multivariate Kernel Density Estimation

Abstract

This paper develops a method to obtain multivariate kernel functions for density estimation problems in which the density function is defined on compact support. If domain-specific knowledge requires certain conditions to be satisfied at the boundary of the support of an unknown density, the proposed method incorporates the information contained in the boundary conditions into the kernel density estimators. The proposed method provides an exact kernel function that satisfies the boundary conditions, even for small samples. Existing methods primarily deal with a one-sided boundary in a one-dimensional problem. We consider density in a two-sided interval and extend it to a multi-dimensional problem.

Keywords

• kernel density estimation
• multivariate density function
• compact support
• boundary conditions
• nonparametric estimation
• heat equation