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Statistica Sinica 21 (2011), 571-596





A NUMERICAL APPROACH TO PERFORMANCE

ANALYSIS OF QUICKEST

CHANGE-POINT DETECTION PROCEDURES


George V. Moustakides$^1$, Aleksey S. Polunchenko$^2$ and
Alexander G. Tartakovsky$^2$


$^1$University of Patras and $^2$University of Southern California


Abstract: For the most popular sequential change detection rules such as CUSUM, EWMA, and the Shiryaev-Roberts test, we develop integral equations and a concise numerical method to compute a number of performance metrics, including average detection delay and average time to false alarm. We pay special attention to the Shiryaev-Roberts procedure and evaluate its performance for various initialization strategies. Regarding the randomized initialization variant proposed by Pollak, known to be asymptotically optimal of order-3, we offer a means for numerically computing the quasi-stationary distribution of the Shiryaev-Roberts statistic, that is, the distribution of the initializing random variable, thus making this test applicable in practice. A significant side-product of our computational technique is the observation that deterministic initializations of the Shiryaev-Roberts procedure can also enjoy the same order-3 optimality property as Pollak's randomized test and, after careful selection, even uniformly outperform it.



Key words and phrases: Fast initial response, Fredholm integral equation of the second kind, numerical analysis, quasi-stationary distribution, quickest changepoint detection, sequential analysis, Shiryaev-Roberts procedure.

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