scholarly journals Sequential Tests for Composite Hypotheses

2008 ◽  
Keyword(s):  
Sequential Tests ◽  
Composite Hypotheses

scholarly journals On sequential versions of the generalized likelihood ratio test

1979 ◽  
Vol 86 (1) ◽  
pp. 85-90 ◽  
Author(s):  
Andrew D. Barbour
Keyword(s):  
Likelihood Ratio ◽  
Null Hypothesis ◽  
Exponential Family ◽  
Likelihood Ratio Statistic ◽  
Generalized Likelihood Ratio Test ◽  
Ratio Test ◽  
Uhlenbeck Process ◽  
Large Sample ◽  
Sequential Tests ◽  
Composite Hypotheses

AbstractIt 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.

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