On some kernel density estimation bandwidth selectors related to the double kernel method

Jones, M. C. (1998). On some kernel density estimation bandwidth selectors related to the double kernel method. Sankhya (Series A), 60(2) pp. 249–264.

URL: http://www.jstor.org/stable/25051201

Abstract

We explore an L₂ modification of an L₁-based method for automatic band width 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 L₂ double kernel method does not provide the expected improvement in quality of estimating the 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.

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