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September, 1980 Risk of Asymptotically Optimum Sequential Tests
Gloria C. Zerdy
Ann. Statist. 8(5): 1110-1122 (September, 1980). DOI: 10.1214/aos/1176345148


The problem considered is that of testing sequentially between two separated composite hypotheses concerning the mean of a normal distribution with known variance. The parameter space is the real line, on which is assumed an a priori distribution, $W,$ with full support. A family $\{\delta(c)\}$ of sequential tests is defined and shown to be asymptotically Bayes, as the cost, $c$, per observation tends to zero, relative to a large class of fully supported a priori distributions. The ratio of the integrated risk of the Bayes procedure to that of $\delta(c)$ is shown to be $1 - 0(\log\log c^{-1}/\log c^{-1})$, as $c$ tends to zero, for every $W.$


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Gloria C. Zerdy. "Risk of Asymptotically Optimum Sequential Tests." Ann. Statist. 8 (5) 1110 - 1122, September, 1980.


Published: September, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0452.62068
MathSciNet: MR585709
Digital Object Identifier: 10.1214/aos/1176345148

Primary: 62L10
Secondary: 62F05

Rights: Copyright © 1980 Institute of Mathematical Statistics


Vol.8 • No. 5 • September, 1980
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