A Numerical Approach to Performance Analysis of Quickest Change-Point Detection Procedures
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.
Cite
@article{arxiv.0907.3521,
title = {A Numerical Approach to Performance Analysis of Quickest Change-Point Detection Procedures},
author = {George V. Moustakides and Aleksey S. Polunchenko and Alexander G. Tartakovsky},
journal= {arXiv preprint arXiv:0907.3521},
year = {2011}
}
Comments
32 pages, to appear in Statistica Sinica