Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 2, pp. 249-264

ON SOME KERNEL DENSITY ESTIMATION BANDWIDTH SELECTORS RELATED TO THE DOUBLE KERNEL METHOD

By

M.C. JONES, The Open University, Milton Keynes

SUMMARY. We explore an $L_2$ modification of an $L_1$--based method for automatic bandwidth selection for kernel density estimation called the double kernel method (Devroye, 1989). The method uses up to two bandwidths, $g$ and $h$, in objective function estimation. When $g=h$, we observe close relationships with a particular useful class of objective functions that contains two existing bandwidth selection methods as special cases, and are led to links with higher order kernels and bias correction. When $g >>h$, the $L_2$ double kernel method does not provide the expected improvement in quality of estimating the {\it mean} integrated squared error (MISE) optimal bandwidth. Instead, it stays close to its roots in estimating the ISE optimal bandwidth and provides a particularly good estimator thereof.

AMS (1991) subject classification.62G07.

Key words and phrases. Biased cross--validation, bootstrap bandwidth selection, kernel smoothing, (mean) integrated squared error, L2 methods, Sheather--Jones bandwidth.

Full paper (PDF)

This article in Mathematical Reviews