Boundary adjusted density estimation and bandwidth selection

This paper studies boundary effects of the kernel density estimation and pr oposes some remedies to the problems. Since the kernel estimate is designed for estimating a smooth density, it introduces a large bias near the bound aries where the density is discontinuous. Bandwidth selectors developed for the kernel estimate that select a small bandwidth to reduce the bias can d ramatically increase the variation and roughness of the density estimate. I n this paper, several boundary adjusted procedures for estimating the densi ty, as well as selecting the bandwidth, are introduced. The proposed proced ures greatly reduce the boundary effects and is shown that these density es timates have the same optimal convergence rate as that of the kernel densit y estimate of a smooth density. Some asymptotic results about the boundary adjusted procedures are provided. Simulation studies were carried out to ch eck the empiric performance of the proposed procedures compared to some exi sting boundary-corrected estimation procedures. In general, simulation resu lts indicate that for moderate to large sample sizes, the proposed procedur es reduce the boundary Effects substantially, and are better than comparabl e existing methods. As an example, we estimate a relevant density connected with some coal-mining disaster data.