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Activity Number: 139
Type: Contributed
Date/Time: Monday, August 4, 2008 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Computing
Abstract - #302332
Title: Extending the Range of Application for Generalized Goodness-of-Fit Statistics
Author(s): Leah Jager*+
Companies: U.S. Naval Academy
Address: Department of Mathematics, Annapolis, MD, 21402,
Keywords: goodness-of-fit ; multiple testing ; recursive methods ; finite sample calculations
Abstract:

Jager and Wellner (2007) introduce a generalized family of statistics for the classical goodness-of-fit problem. The asymptotic null distribution of these statistics is derived, but is not accurate for samples sizes smaller than 1,000,000. Owen (1995) developed a method for calculating exact null quantiles of the Berk-Jones statistic in samples sizes smaller than 1,000. This method can be extended to the generalized statistics, but still leaves a range of sample sizes where the statistics cannot be accurately applied. Applications of these statistics to large-scale multiple testing problems found in genetics and genomics typically involve sample sizes in this problematic range. We discuss extension of Owen's method to the generalized statistics and to sample sizes up to 10,000. These exact results are used to form approximations in the range between the exact and asymptotic methods.


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