On optimality of the Shiryaev-Roberts procedure for detecting a change in distribution

By Aleksey S. Polunchenko, Alexander G. Tartakovsky. 2009

98 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f4547e05c31f3bab60a78aeb6547f55b286ce27b

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In Statistics and Probability

Citations in the corpus

Third-order Asymptotic Optimality of the Generalized Shiryaev-Roberts Changepoint Detection Procedures (2010, methodology): “Examples where the SR–r procedure is strictly minimax are provided by Polunchenko and Tartakovsky [10] and Tartakovsky and Polunchenko [14].”
Some Current Directions in the Theory and Application of Statistical Process Monitoring (2014, background): “See, for example, Tartakovsky and Veeravalli (2004), Mei (2006), Siegmund and Yakir (2008), and Polunchenko and Tartakovsky (2010).”