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Weak approximations of the empirical process when parameters are estimated

  • M. Csörgő
  • M. D. Burke
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 566)

Abstract

Strong approximation results and methodology are used to obtain in-probability representations of the empirical process when the parameters of the underlying distribution function are estimated. These representations are obtained under a null hypothesis and a sequence of alternatives converging to the null hypothesis. The fairly general conditions on the estimators are often satisfied by maximum likelihood estimators. The asymptotic distribution of the estimated empirical process depends, in general, on the true value of the unknown parameters. Some useful methods of overcoming this difficulty are discussed.

Keywords

Gaussian Process Maximum Likelihood Estimator Empirical Process Fisher Information Matrix Strong Approximation 
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.

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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • M. Csörgő
    • 1
  • M. D. Burke
    • 1
  1. 1.Department of MathematicsCarleton UniversityOttawaCanada

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