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March, 1983 An Efficient Approximate Solution to the Kiefer-Weiss Problem
Michael D. Huffman
Ann. Statist. 11(1): 306-316 (March, 1983). DOI: 10.1214/aos/1176346081


The problem is to decide on the basis of repeated independent observations whether $\theta_0$ or $\theta_1$ is the true value of the parameter $\theta$ of a Koopman-Darmois family of densities, where the error probabilities are at most $\alpha_0$ and $\alpha_1$. An explicit method is derived for determining a combination of one-sided SPRT's, known, as a 2-SPRT, which minimizes the maximum expected sample size to within $o((\log \alpha^{-1}_0)^{1/2})$ as $\alpha_0$ and $\alpha_1$ go to 0, subject to the condition that $0 < C_1 < \log \alpha_0/\log\alpha_1 < C_2 < \infty$ for fixed but arbitrary constants $C_1$ and $C_2$. For the case of testing the mean of an exponential density, extensive computer calculations comparing the proposed 2-SPRT with optimal procedures show that the 2-SPRT comes within 2% of minimizing the maximum expected sample size over a broad range of error probability and parameter values.


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Michael D. Huffman. "An Efficient Approximate Solution to the Kiefer-Weiss Problem." Ann. Statist. 11 (1) 306 - 316, March, 1983.


Published: March, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0521.62065
MathSciNet: MR684888
Digital Object Identifier: 10.1214/aos/1176346081

Primary: 62L10
Secondary: 62F03

Keywords: 2-SPRT , Asymptotic efficiency , sequential probability ratio test

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 1 • March, 1983
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