Exact Mean and Mean Squared Error of the Smoothed Bootstrap Mean Integrated Squared Error Estimator
Johns Hopkins University
DSO National Laboratories - Signal Processing Laboratory
Computational Statistics, Vol. 15, No. 2, Pp. 169-181, 2000
New expressions are obtained for the mean and mean squared error of the smoothed bootstrap mean integrated squared error estimator in Gaussian kernel estimation of normal mixture densities. The use of such densities is in the same spirit as Marron and Wand (1992) and provides the same benefits. The resulting expressions are easily computable and describe the exact behavior of the estimator, thus complementing known asymptotic results for it. They reveal important information for small samples, not indicated by asymptotics. In particular, while asymptotics call for oversmoothing the estimator, undersmoothing may actually be more appropriate for small samples.
Keywords: bandwidth selection, kernel estimator, nonparametric density estimation, normal mixtures, pilot bandwidth selection, smoothed crossvalidation
JEL Classification: C15
Date posted: January 22, 2001