OPTIMAL BANDWIDTH SELECTION FOR DECONVOLUTED KERNEL DENSITY ESTIMATION USING BOOTSTRAP METHOD
Abstract
To estimate an unknown density when observed measurements are from the
convolution model contaminated by additive measurement errors, Stefanski and
Carroll (1990) proposed using Fourier inversion on the product of Fourier transform of
a kernel function and the characteristic function of the error variable. One important
element in constructing such a density estimator is the bandwidth. The goal of this
research is to establish an optimal bandwidth so that the mean integrated squared
error of the estimator is minimized. The bootstrap method is used to accomplish this
goal. The simulation results show that the estimated optimal bandwidths provide
adequate estimation to the unknown densities.