Abstract #301132

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JSM 2002 Abstract #301132
Activity Number: 321
Type: Contributed
Date/Time: Wednesday, August 14, 2002 : 12:00 PM to 1:50 PM
Sponsor: Section on Statistical Computing*
Abstract - #301132
Title: Exact Mean and Variance of Bickel-Rosenblatt Goodness-of-Fit Statistic
Author(s): Wei-Min Huang*+
Affiliation(s): Lehigh University
Address: 14 East Packer Avenue, Bethlehem, Pennsylvania, 18015, USA
Keywords: kernel density estimation ; density estimates in tests ; goodness-of-fit statistics ; uniform kernel ; smoothed chi-square tests ; asymptotic power
Abstract:

Bickel and Rosenblatt introduced several goodness-of-fit statistics (Ann. Statist.,1071-1095,1973). These statistics are based on kernel density estimates. It has been shown that quadratic form-type kernel-based goodness-of-it statistics have optimal properties under uniform kernel (Ann. Statist., 999-1009,1991). In this paper, the exact mean and variance of a quadratic Bickal-Rosenblatt statistic under the uniform kernel are shown. Applications for improving the large-sample distribution of the goodness-of-fit statistics are mentioned. Simulation and other related issues are also included in the paper.

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