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June, 1985 Robust Sequential Testing
Pham Xuan Quang
Ann. Statist. 13(2): 638-649 (June, 1985). DOI: 10.1214/aos/1176349544

Abstract

This paper considers the asymptotic minimax property of the sequential probability ratio test (SPRT) when the given distributions $P_{\pm \varepsilon}$ contain a small amount of contamination. Let $\mathscr{P}_{\pm \varepsilon}$ be the neighborhoods of $P_{\pm \varepsilon}.$ Suppose that $P_\varepsilon$ and $P_{-\varepsilon}$ approach each other as $\varepsilon \downarrow 0$ and that $\mathscr{P}_{\pm \varepsilon}$ shrink at an appropriate rate. We prove (under regularity assumptions) that the SPRT based on the least favorable pair of distributions $(Q^\ast_{-\varepsilon}, Q^\ast_\varepsilon)$ given by Huber (1965) is asymptotically least favorable for expected sample size and is asymptotically minimax, provided that the limiting maximum error probabilities do not exceed $1/2.$

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Pham Xuan Quang. "Robust Sequential Testing." Ann. Statist. 13 (2) 638 - 649, June, 1985. https://doi.org/10.1214/aos/1176349544

Information

Published: June, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0588.62136
MathSciNet: MR790562
Digital Object Identifier: 10.1214/aos/1176349544

Subjects:
Primary: 62F35
Secondary: 62L10

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 2 • June, 1985
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