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Likelihood ratio tests for sequential k-decision problems

Lorden, Gary (1972) Likelihood ratio tests for sequential k-decision problems. Annals of Mathematical Statistics, 43 (5). pp. 1412-1427. ISSN 0003-4851.

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Sequential tests of separated hypotheses concerning the parameter θ of a Koopman-Darmois 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
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1670
Deposited By: Tony Diaz
Deposited On:03 May 2006
Last Modified:26 Dec 2012 08:45

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