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December, 1983 The Effect of Dependence on Chi-Squared and Empiric Distribution Tests of Fit
Leon J. Gleser, David S. Moore
Ann. Statist. 11(4): 1100-1108 (December, 1983). DOI: 10.1214/aos/1176346324


Suppose that a test of fit to a parametric family of distributions is employed, with critical points determined from the limiting null distribution of the test statistic for IID observations. It is shown that if the observations are in fact a stationary process satisfying a positive dependence condition, the test will reject a true null hypothesis too often. This result is established for a broad class of chi squared and empiric df tests, including the Pearson, Kolmogorov-Smirnov and Cramer-von Mises tests with general estimators of unknown parameters. Furthermore, the method of proof is sufficiently general to apply also to other classes of tests. Confounding of positive dependence with lack of fit is therefore a general phenomenon in the use of omnibus tests of fit.


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Leon J. Gleser. David S. Moore. "The Effect of Dependence on Chi-Squared and Empiric Distribution Tests of Fit." Ann. Statist. 11 (4) 1100 - 1108, December, 1983.


Published: December, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0549.62032
MathSciNet: MR720256
Digital Object Identifier: 10.1214/aos/1176346324

Primary: 62G10
Secondary: 60G10

Rights: Copyright © 1983 Institute of Mathematical Statistics


Vol.11 • No. 4 • December, 1983
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