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Biometrika 1989 76(4):705-712; doi:10.1093/biomet/76.4.705
© 1989 by Biometrika Trust
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Bootstrap choice of the smoothing parameter in kernel density estimation

CHARLES C. TAYLOR

Department of Mathematics, University of Strathclyde Glasgow, G1 1XH, U.K.

Cross-validation based on integrated squared error has already been applied to the choice of smoothing parameter in the kernel method of density estimation. In this paper, an alternative resampling plan, based on the bootstrap, is proposed in an attempt to estimate mean integrated squared error. This leads to a further data-based choice of smoothing parameter. The two methods are compared and some simulations and examples demonstrate the relative merits. For large samples, the bootstrap performs better than cross-validation for many distributions.

Key Words: Cross-validation • Mean integrated squared error • Resampling • Smoothed bootstrap


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