Power of the MOSUM test for online detection of a transient change in mean. Issue 2 (2nd April 2020)

• Record Type: Journal Article
• Authors: Noonan, Jack; Zhigljavsky, Anatoly
• Is Part Of: Sequential analysis. Volume 39:Issue 2(2020)
• Page Start: 269
• Page End: 293
• Publication Date: 2020-04-02
• Subjects: Boundary crossing probability -- change point detection -- moving sum -- moving sum of normal; 60G50 -- 60G35; 60G70 -- 94C12 -- 93E20; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2020.1767406
• Languages: English
• ISSNs: 0747-4946

Abstract

Abstract: In this article we discuss an online moving sum (MOSUM) test for detection of a transient change in the mean of a sequence of independent and identically distributed (i.i.d.) normal random variables. By using a well-developed theory for continuous time Gaussian processes and subsequently correcting the results for discrete time, we provide accurate approximations for the average run length (ARL) and power of the test. We check theoretical results against simulations, compare the power of the MOSUM test with that of the cumulative sum (CUSUM), and briefly consider the cases of nonnormal random variables and weighted sums.