## The Annals of Statistics

- Ann. Statist.
- Volume 13, Number 2 (1985), 638-649.

### Robust Sequential Testing

#### 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 $1/2.$

#### Article information

**Source**

Ann. Statist., Volume 13, Number 2 (1985), 638-649.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176349544

**Digital Object Identifier**

doi:10.1214/aos/1176349544

**Mathematical Reviews number (MathSciNet)**

MR790562

**Zentralblatt MATH identifier**

0588.62136

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62F35: Robustness and adaptive procedures

Secondary: 62L10: Sequential analysis

**Keywords**

Sequential probability ratio test shrinking neighborhoods asymptotic minimax

#### Citation

Quang, Pham Xuan. Robust Sequential Testing. Ann. Statist. 13 (1985), no. 2, 638--649. doi:10.1214/aos/1176349544. https://projecteuclid.org/euclid.aos/1176349544