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Open-ended tests for Koopman-Darmois families

Lorden, Gary (1973) Open-ended tests for Koopman-Darmois families. Annals of Statistics, 1 (4). pp. 633-643. ISSN 0090-5364. http://resolver.caltech.edu/CaltechAUTHORS:LORas73

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Abstract

The generalized likelihood ratio is used to define a stopping rule for rejecting the null hypothesis θ = θ0 in favor of θ > θ0. Subject to a bound α on the probability of ever stopping in case θ = θ0, the expected sample sizes for θ > θ0 are minimized within a multiple of log log α-1, the multiple depending on θ. An heuristic bound on the error probability of a likelihood ratio procedure is derived and verified in the case of a normal mean by consideration of a Wiener process. Useful lower bounds on the small-sample efficiency in the normal case are thereby obtained.


Item Type:Article
Additional Information:© 1973 Institute of Mathematical Statistics. Received November 1970; revised October 1972.
Subject Keywords:Likelihood ratio, sequential probability ratio test, open-ended test, asymptotic efficiency
Record Number:CaltechAUTHORS:LORas73
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:LORas73
Alternative URL:http://links.jstor.org/sici?sici=0090-5364%28197307%291%3A4%3C633%3AOTFKF%3E2.0.CO%3B2-N
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7237
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:23 Jan 2007
Last Modified:26 Dec 2012 09:30

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