On Pseudodata Methods for Removing Boundary Effects in Kernel Density Estimation

Abstract

SUMMARY We suggest a method for boundary correcting kernel density estimators, based on generating pseudodata beyond the extremities of the density's support. The estimator produced in this way enjoys optimal orders of bias and variance right up to the ends of the support, and it may be used with kernels of arbitrary order. Our method is considerably more adaptive than the common data reflection approach, which is not really appropriate for kernels of order 2 or more since it does not adequately correct boundary bias. In a simulation study, for densities on [0,1] with positive slope at x = 0, our method was found to have lower mean-squared error at x = 0 than the boundary kernel method, especially for small sample sizes. Our technique may be used in conjunction with plug-in or least squares cross-validation methods of bandwidth selection and has an analogue in the context of estimating a point process intensity.