ON nonparametric density estimation at the boundary

Boundary effects are well known to occur in nonparametric density estimation when the support of the density has a finite endpoint. The usual kernel density estimators require modifications when estimating the density near endpoints of the support. In this paper, we propose a new and intuitive method of removing boundary effects in density estimation. Our idea, which replaces the unwanted terms in the bias expansion by their estimators, offers new ways of constructing boundary kernels and optimal endpoint kernels. We also discuss the choice of bandwidth variation functions at the boundary region. The performance of our results are numerically analyzed in a Monte Carlo study.