A NUMERICAL APPROACH TO PERFORMANCE ANALYSIS OF QUICKEST CHANGE-POINT DETECTION PROCEDURES

作者：Moustakides George V^*; Polunchenko Aleksey S; Tartakovsky Alexander G

来源：Statistica Sinica, 2011, 21(2): 571-596.

DOI：10.5705/ss.2011.026a

• Fast initial response
• Fredholm integral equation of the second kind
• numerical analysis
• quasi-stationary distribution
• quickest changepoint detection
• sequential analysis
• Shiryaev-Roberts procedure

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.

• 出版日期2011-4