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On a test for goodness-of-fit based on the empirical probability measure of Foutz and testing for exponentiality

Part of the Lecture Notes in Mathematics book series (LNM,volume 861)

Abstract

Foutz (1979) proposed a goodness-of-fit test for the simple hypothesis specifying a continuous p-variate distribution . For a suitably defined empirical probability measure, , the proposed test is based on the supremum of the absolute differences between hypothesized and empirical probabilities, the supremum being taken over all possible events. He showed that his test statistic was distribution free in the general p-variate case and derived its asymptotic null distribution. Here an alternate quick way of deriving the latter is proposed and connections are made to testing for exponentiality.

Keywords

  • Brownian Bridge
  • Quantile Process
  • Equivalent Block
  • Mise Type
  • Borel Class

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This research was supported by a Canada Council Killam Senior Research Fellowship and by a Natural Sciences and Engineering Research Council Canada Operating Grant, both held at Carleton University, Ottawa.

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References

  1. Anderson, T.W. (1966). Some nonparametric procedures based on statistically equivalent blocks. Proc. Internat. Symp. Multivariate Anal. (P.R. Krishnaiah, ed.). 5–27, Academic Press, New York.

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  2. Csörgő, M.-Révész, P. (1978). Strong approximations of the quantile process. Ann. Statist. 6, 882–894.

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  3. Csörgő, M.-Révész, P. (1979). Quadratic...ity tests. Carleton Mathematical Series No. 162. A revised version is to appear.

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  4. Csörgő, M., Seshadri, V. and Yalovsky, M. (1975). Applications of characterizations in the area of goodness-of-fit. In Statistical Distributions in Scientific Work, Vol. 2, 79–90, eds. G.P. Patil et al. D. Reidel Publishing Co., Dordrecht-Holland.

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  5. Foutz, Robert V. (1979). A test for goodness-of-fit based on an empirical probability measure. To appear.

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© 1981 Springer-Verlag

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Csörgő, M. (1981). On a test for goodness-of-fit based on the empirical probability measure of Foutz and testing for exponentiality. In: Dugué, D., Lukacs, E., Rohatgi, V.K. (eds) Analytical Methods in Probability Theory. Lecture Notes in Mathematics, vol 861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097309

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  • DOI: https://doi.org/10.1007/BFb0097309

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  • Print ISBN: 978-3-540-10823-8

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