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June, 1988 Nearly Optimal Sequential Tests of Composite Hypotheses
Tze Leung Lai
Ann. Statist. 16(2): 856-886 (June, 1988). DOI: 10.1214/aos/1176350840


A simple class of sequential tests is proposed for testing the one-sided composite hypotheses $H_0: \theta \leq \theta_0$ versus $H_1: \theta \geq \theta_1$ for the natural parameter $\theta$ of an exponential family of distributions under the 0-1 loss and cost $c$ per observation. Setting $\theta_1 = \theta_0$ in these tests also leads to simple sequential tests for the hypotheses $H: \theta < \theta_0$ versus $K: \theta > \theta_0$ without assuming an indifference zone. Our analytic and numerical results show that these tests have nearly optimal frequentist properties and also provide approximate Bayes solutions with respect to a large class of priors. In addition, our method gives a unified approach to the testing problems of $H$ versus $K$ and also of $H_0$ versus $H_1$ and unifies the different asymptotic theories of Chernoff and Schwarz for these two problems.


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Tze Leung Lai. "Nearly Optimal Sequential Tests of Composite Hypotheses." Ann. Statist. 16 (2) 856 - 886, June, 1988.


Published: June, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0657.62088
MathSciNet: MR947582
Digital Object Identifier: 10.1214/aos/1176350840

Primary: 62L10
Secondary: 62L05, 62L15

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 2 • June, 1988
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