2017/06/02 by Aleksey S. Polunchenko, Polunchenko, Aleksey S., Vasanthan Raghavan +1
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #Computation (stat.CO) #FOS: Computer and information sciences #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1706.00824
openalex publication_date 2017/06/02 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We consider the problem of quickest change-point detection where the\nobservations form a first-order autoregressive (AR) process driven by\ntemporally independent standard Gaussian noise. Subject to possible change are\nboth the drift of the AR(1) process (\μ) as well as its correlation\ncoefficient (\λ), both known. The change is abrupt and persistent, and\nis of known magnitude, with vert\λ vert<1 throughout. For this\nscenario, we carry out a comparative performance analysis of the popular\nCumulative Sum (CUSUM) chart and its less well-known but worthy competitor --\nthe Shiryaev-Roberts (SR) procedure. Specifically, the performance is measured\nthrough Pollak's Supremum (conditional) Average Delay to Detection (SADD)\nconstrained to a pre-specified level of the Average Run Length (ARL) to false\nalarm. Particular attention is drawn to the sensitivity of each procedure's\nSADD and ARL with respect to the value of \λ before and after the\nchange. The performance is studied through the solution of the respective\nintegral renewal equations obtained via Monte Carlo simulations. The\nsimulations are designed to estimate the sought performance metrics in an\nunbiased and asymptotically strongly consistent manner, and to within a\nprescribed proportional closeness (also asymptotically). Our extensive\nnumerical studies suggest that both the CUSUM chart and the SR procedure are\nasymptotically second-order optimal, even though the CUSUM chart is found to be\nslightly better than the SR procedure, irrespective of the model parameters.\nMoreover, the existence of a worst-case post-change correlation parameter\ncorresponding to the poorest detectability of the change for a given ARL to\nfalse alarm is established as well. To the best of our knowledge, this is the\nfirst time the performance of the SR procedure is studied for autocorrelated\ndata.\n