頁籤選單縮合
題 名 | A Numerical Approach to Performance Analysis of Quickest Change-Point Detection Procedures |
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作 者 | Moustakides, George V.; Polunchenko, Aleksey S.; Tartakovsky, Alexander G.; | 書刊名 | Statistica Sinica |
卷 期 | 21:2 2011.04[民100.04] |
頁 次 | 頁571-596 |
分類號 | 319.5 |
關鍵詞 | Fast initial response; Fredholm integral equation of the second kind; Numerical analysis; Quasi-stationary distribution; Quickest changepoint detection; Sequential analysis; Shiryaev-Roberts procedure; |
語 文 | 英文(English) |
英文摘要 | 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. |
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