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Characterizations and Goodness of Fit Tests

Federico J. O'Reilly and Michael A. Stephens
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 44, No. 3 (1982), pp. 353-360
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2345491
Page Count: 8
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Characterizations and Goodness of Fit Tests
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Abstract

In this article a systematic approach to providing goodness of fit tests is discussed, for the composite goodness of fit problem of testing that the distribution F of a random sample comes from a parametric family F0. Characterization procedures are emphasized, and it is shown that, at least for the exponential case, invariant characterizations appear to be better than those which are not invariant. A general technique is developed for producing invariant characterizations and for the exponential case it is shown how these are related to characterizations already in the literature. Power studies are given to examine the tests based on both invariant and non-invariant characterizations.

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