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Activity Number:
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207
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Type:
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Contributed
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Date/Time:
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Monday, August 7, 2006 : 2:00 PM to 3:50 PM
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Sponsor:
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IMS
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| Abstract - #306410 |
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Title:
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Goodness-of-Fit Tests via Phi-Divergences
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Author(s):
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Leah R. Jager*+ and Jon A. Wellner
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Companies:
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University of Washington and University of Washington
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Address:
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5705 Phinney Ave. N., Apt. 206, Seattle, WA, 98103,
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Keywords:
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goodness-of-fit ; phi-divergence ; Poisson boundaries ; multiple comparisons
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Abstract:
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We introduce a unified family of goodness-of-fit statistics that includes both the supremum version of the Anderson-Darling statistic and the test statistic of Berk and Jones (1979) as special cases. The family is based on phi-divergences somewhat analogously to the tests for multinomial families introduced by Cressie and Read (1984). We show that the asymptotic null distribution theory for the Anderson-Darling and Berk-Jones statistics extends to the entire family. We describe necessary and sufficient conditions for the statistics to converge to their natural parameters under fixed alternatives, and show that the family exhibits Poisson boundary behavior for certain extreme alternatives. We prove that this family achieves the same optimal detection boundary as Tukey's higher criticism statistic for normal shift mixture alternatives, as discussed in Donoho and Jin (2004).
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