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July, 1973 Open-Ended Tests for Koopman-Darmois Families
Gary Lorden
Ann. Statist. 1(4): 633-643 (July, 1973). DOI: 10.1214/aos/1176342459


The generalized likelihood ratio is used to define a stopping rule for rejecting the null hypothesis $\theta = \theta_0$ in favor of $\theta > \theta_0$. Subject to a bound $\alpha$ on the probability of ever stopping in case $\theta = \theta_0$, the expected sample sizes for $\theta > \theta_0$ are minimized within a multiple of $\log \log \alpha^{-1}$, the multiple depending on $\theta$. 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.


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Gary Lorden. "Open-Ended Tests for Koopman-Darmois Families." Ann. Statist. 1 (4) 633 - 643, July, 1973.


Published: July, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0282.62072
MathSciNet: MR426318
Digital Object Identifier: 10.1214/aos/1176342459

Primary: 62L10

Keywords: Asymptotic efficiency , likelihood ratio , open-ended test , sequential probability ratio test

Rights: Copyright © 1973 Institute of Mathematical Statistics


Vol.1 • No. 4 • July, 1973
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