Likelihood ratio tests for sequential k-decision problems
- Creators
- Lorden, Gary
Abstract
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.
Additional Information
Received November 4, 1970; revised January 1972. The author wishes to thank the referee for helpful suggestions.Files
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Additional details
- Eprint ID
- 1670
- Resolver ID
- CaltechAUTHORS:LORams72
- Created
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2006-05-03Created from EPrint's datestamp field
- Updated
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2019-10-02Created from EPrint's last_modified field