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On sequential versions of the generalized likelihood ratio test

Published online by Cambridge University Press:  24 October 2008

Andrew D. Barbour
Andrew D. Barbour
Affiliation:
Gonville and Caius College, Cambridge
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Abstract

It is shown that the Wilks large sample likelihood ratio statistic λn, for testing between composite hypotheses Θ0 ⊂ Θ1 on the basis of a sample of size n, behaves as n varies like a diffusion process related to an equilibrium Ornstein-Uhlenbeck process, whenever the null hypothesis is true. This fact is used to construct large sample sequential tests based on λn, which are the same whatever the underlying distributions. In particular, the underlying distributions need not belong to an exponential family.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 1 , July 1979 , pp. 85 - 90
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

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