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Exact Mean and Mean Squared Error of the Smoothed Bootstrap Mean Integrated Squared Error Estimator

Posted: 22 Jan 2001  

Carey Priebe

Johns Hopkins University

Dominic Lee

DSO National Laboratories - Signal Processing Laboratory

Abstract

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

Suggested Citation

Priebe, Carey and Lee, Dominic, Exact Mean and Mean Squared Error of the Smoothed Bootstrap Mean Integrated Squared Error Estimator. Computational Statistics, Vol. 15, No. 2, Pp. 169-181, 2000. Available at SSRN: https://ssrn.com/abstract=235423

Carey Priebe (Contact Author)

Johns Hopkins University ( email )

Dept. of Mathematical Sciences
Baltimore, MD 21218
United States
410-516-7198 (Phone)
410-516-7459 (Fax)

Dominic Lee

DSO National Laboratories - Signal Processing Laboratory ( email )

20 Science Park Drive
Singapore, 118230
(65)7727176 (Phone)
(65)7759011 (Fax)

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