Variable kernel density estimation
by
Martin Hazelton
University of Western Australia

The potential advantages of using variable bandwidths (which adapt to local smoothing requirements) in kernel density estimation have long been recognized, but development of such technology has proved problematic. We discuss a technique for selecting sample-point bandwidths, based upon a cubic spline representation of the log-bandwidth function. This type of approach has been tried with success in related problems, but there is devil in the detail in the application of this methodology to variable bandwidth selection. We attempt to optimize the tuning parameters of our methodology through numerical testing rather than asymptotic analysis, since we have some reason to distrust the practical usefulness of the latter approach.

Date received: April 3, 2002