Title

Weighted Hellinger Distance As An Error Criterion For Bandwidth Selection In Kernel Estimation

Keywords

Bandwidth selection; Cross-validation; Distribution function; Hellinger distance; Integrated mean-square error; Kernel estimation; Probability density function

Abstract

Ever since the pioneering work of Parzen [Parzen, E., 1962, On estimation of a probability density function and mode. Annales of Mathematics and Statistics , 33, 1065-1076.], the mean-square error (MSE) and its integrated form (MISE) have been used as the criteria of error in choosing the window size in kernel density estimation. More recently, however, other criteria have been advocated as competitors to the MISE, such as the mean absolute deviation or the Kullback-Leibler loss. In this note, we define a weighted version of the Hellinger distance and show that it has an asymptotic form, which is one-fourth the asymptotic MISE under a slightly more stringent smoothness conditions on the density f . In addition, the proposed criteria give rise to a new way for data-dependent bandwidth selection, which is more stable in the sense of having smaller MSE than the usual least-squares cross-validation, biased cross-validation or the plug-in methodologies when estimating f . Analogous results for the kernel distribution function estimate are also presented.

Publication Date

2-1-2006

Publication Title

Journal of Nonparametric Statistics

Volume

18

Issue

2

Number of Pages

215-226

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1080/10485250600712008

Socpus ID

33745061925 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/33745061925

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