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Activity Number:
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445
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Type:
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Contributed
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Date/Time:
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Thursday, August 7, 2003 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #300880 |
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Title:
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Interval-based PP Plot: A Graphical Tool to Localize Regions of Lack of Fit
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Author(s):
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Heidi Wouters*+ and Olivier Thas and Jean-Pierre Ottoy
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Companies:
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University of Ghent and University of Ghent and Ghent University
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Address:
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Coupure Links 653, Ghent, , B-9000, Belgium
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Keywords:
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goodness-of-fit ; Watson test ; smooth tests ; EDF tests
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Abstract:
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For the one-sample goodness-of-fit problem, many different types of tests have been proposed. Two well-known types are the empirical distribution function (EDF) and the smooth tests. It has been shown that each EDF statistic is related to a specific smooth family of alternatives. In particular, each term in a decomposition of the EDF statistic corresponds to one parameter in the smooth family. We present this link for the Watson statistic, which was originally proposed for the goodness-of-fit problem on the line. We show that each component of the Watson statistic now corresponds with two parameters in a smooth family. Our results show that this particular characteristic makes the Watson test very powerful for "local'' deviation from the null model ("local'' is used here in the sense that the deviation from the null model is localized only in a small subset of the support). Finally, we use our results to extend the PP plot to an interval-based PP plot, which is a graphical tool to assess goodness-of-fit and which allows a good localization of the region of poor goodness-of-fit.
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