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.
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