Abstract #300700


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JSM 2002 Abstract #300700
Activity Number: 71
Type: Contributed
Date/Time: Monday, August 12, 2002 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics*
Abstract - #300700
Title: A Weighted Hellinger Distance as an Error Criterion for Bandwidth Selection in Kernel Estimation
Author(s): Abdel-Razzaq Mugdadi*+ and Ibrahim Ahmad
Affiliation(s): Southern Illinois University and University of Central Florida
Address: , Carbondale, Illinois, 62901-4408,
Keywords: Hellinger distance ; kernel estimation ; bandwidth selection ; least square cross validation
Abstract:

Ever since the poineering work of Parzen in 1962, the MSE and the MISE are used as criteria of error in choosing the bandwidth in kernel density estimation. More recently, however, other criteria have been advocated as competitors to the MISE. For example, Kanazawa in 1993 advocated the use of the Hellinger distance as an error criterion for window size choice. This distance works only for compactly supported densities. 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 condition on f (or F). In addition, the proposed criteria gives rise to a new way for data-dependent bandwidth selection, which is more stable than the usual least-squares cross validation.


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