Lorden, Gary (1972) Likelihood ratio tests for sequential kdecision problems. Annals of Mathematical Statistics, 43 (5). pp. 14121427. ISSN 00034851. http://resolver.caltech.edu/CaltechAUTHORS:LORams72

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Abstract
Sequential tests of separated hypotheses concerning the parameter θ of a KoopmanDarmois family are studied from the point of view of minimizing expected sample sizes pointwise in θ subject to error probability bounds. Sequential versions of the (generalized) likelihood ratio test are shown to exceed the minimum expected sample sizes by at most M log log α(1) uniformly in θ, where α is the smallest error probability bound. The proof considers the likelihood ratio tests as ensembles of sequential probability ratio tests and compares them with alternative procedures by constructing alternative ensembles, applying a simple inequality of Wald and a new inequality of similar type. A heuristic approximation is given for the error probabilities of likelihood ratio tests, which provides an upper bound in the case of a normal mean.
Item Type:  Article 

Additional Information:  Received November 4, 1970; revised January 1972. The author wishes to thank the referee for helpful suggestions. 
Record Number:  CaltechAUTHORS:LORams72 
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:LORams72 
Alternative URL:  http://links.jstor.org/sici?sici=00034851%28197210%2943%3A5%3C1412%3ALRTFSP%3E2.0.CO%3B21 
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ID Code:  1670 
Collection:  CaltechAUTHORS 
Deposited By:  Tony Diaz 
Deposited On:  03 May 2006 
Last Modified:  26 Dec 2012 08:45 
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