Open Access
December 2010 On optimality of the Shiryaev–Roberts procedure for detecting a change in distribution
Aleksey S. Polunchenko, Alexander G. Tartakovsky
Ann. Statist. 38(6): 3445-3457 (December 2010). DOI: 10.1214/09-AOS775


In 1985, for detecting a change in distribution, Pollak introduced a specific minimax performance metric and a randomized version of the Shiryaev–Roberts procedure where the zero initial condition is replaced by a random variable sampled from the quasi-stationary distribution of the Shiryaev–Roberts statistic. Pollak proved that this procedure is third-order asymptotically optimal as the mean time to false alarm becomes large. The question of whether Pollak’s procedure is strictly minimax for any false alarm rate has been open for more than two decades, and there were several attempts to prove this strict optimality. In this paper, we provide a counterexample which shows that Pollak’s procedure is not optimal and that there is a strictly optimal procedure which is nothing but the Shiryaev–Roberts procedure that starts with a specially designed deterministic point.


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Aleksey S. Polunchenko. Alexander G. Tartakovsky. "On optimality of the Shiryaev–Roberts procedure for detecting a change in distribution." Ann. Statist. 38 (6) 3445 - 3457, December 2010.


Published: December 2010
First available in Project Euclid: 30 November 2010

zbMATH: 1204.62141
MathSciNet: MR2766858
Digital Object Identifier: 10.1214/09-AOS775

Primary: 62L10 , 62L15
Secondary: 60G40

Keywords: Changepoint problems , sequential detection , Shiryaev–Roberts procedures

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 6 • December 2010
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