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Abstract:
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Goodness-of-fit testing has enjoyed a resurgence of interest due to applications involving repeated significance testing (or combination of tests) in a variety of applied fields including genomics and astronomy. In this talk I will describe a modification of the goodness of fit statistics proposed by Jager and Wellner (2007) and the use of such test statistics for both goodness of fit and for testing for sparse normal means. The new procedures refine those of Jager and Wellner (2007), and, as special cases, the statistics proposed by Berk and Jones (1979) and Donoho and Jin (2004). Roughly speaking, the high power and accuracy of the procedures of Berk and Jones and Owen in the tail regions of distributions are essentially preserved while gaining considerably in the central region.
This talk is based on recent joint work with Lutz Dumbgen and past work with Leah Jager.
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