ON OPTIMALITY OF THE SHIRYAEV-ROBERTS PROCEDURE FOR DETECTING A CHANGE IN DISTRIBUTION
成果类型：
Article
署名作者：
Polunchenko, Aleksey S.; Tartakovsky, Alexander G.
署名单位：
University of Southern California
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/09-AOS775
发表日期：
2010
页码：
3445-3457
关键词：
摘要：
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.