Abstract
When using kernel-based estimators for probability density functions, a key problem is the choice of smoothing parameter. All existing procedures for this choice suffer from some significant drawback. We propose a simple location-dependent procedure for the choice of smoothing parameters. Initial comparisons with two standard choice methods, due to Parzen and to Breiman et al., with respect to the mean percent error (MPE), show that, while all three methods have comparable performance in estimating unimodal densities, ours and Breiman's both outperform Parzen's in multimodal cases. Since our method is considerably simpler than Breiman's, we develop it further. In particular, through an approximation of the L 1 criterion, we develop a distribution-free goodness-of-fit criterion for evaluating our choice of parameter.
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