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October, 1979 Approximations of the Empirical Process when Parameters are Estimated
M. D. Burke, M. Csorgo, S. Csorgo, P. Revesz
Ann. Probab. 7(5): 790-810 (October, 1979). DOI: 10.1214/aop/1176994939


Almost sure and in-probability representations of the empirical process by appropriate Gaussian processes are obtained when unknown parameters of the underlying distribution function are estimated. As to the method of estimation, we consider maximum likelihood and maximum likelihood-like estimators and construct the above-mentioned representations under a null hypothesis. Similar results are obtained also when using Durbin's more general class of estimators under a sequence of alternatives which converge to the null hypothesis. The resulting Gaussian processes depend, in general, on the true value of the unknown parameters.


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M. D. Burke. M. Csorgo. S. Csorgo. P. Revesz. "Approximations of the Empirical Process when Parameters are Estimated." Ann. Probab. 7 (5) 790 - 810, October, 1979.


Published: October, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0433.62017
MathSciNet: MR542130
Digital Object Identifier: 10.1214/aop/1176994939

Primary: 62E20
Secondary: 60F05 , 60F15 , 60G15 , 62G99 , 62H15

Keywords: composite goodness-of-fit hypotheses , Empirical processes , Kiefer process , Parametric estimation , strong approximations

Rights: Copyright © 1979 Institute of Mathematical Statistics


Vol.7 • No. 5 • October, 1979
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