2015 QPRC

STUDY OF MISMATCHED DETECTION PROCEDURES FOR AUTOCORRELATED DATA

Aleksey S. Polunchenko
Department of Mathematical Sciences, State University of New York at Binghmaton
Binghamton, New York, United States of America
Email: aleksey@math.binghamton.edu

Vasanthan Raghavan
Qualcomm Flarion Technologies, Inc.,
Bridgewater, New Jersey, United States of America
Email: vasanthan_raghavan@ieee.org

Abstract
The focus of this work is on the case where the observations follow an AR(1) process with the drift and/or the correlation coefficient changing at an unknown point in time. While the Cumulative Sum (CUSUM) chart has been studied for the quick detection of this changepoint, more recent focus has been on a competing alternate procedure based on the work of Shiryaev and Roberts; see, e.g., Shiryaev (1961, 1963); Roberts (1966). By studying the Supremum (conditional) Average Detection Delay (SADD) subject to a constraint on the Average Run Length (ARL) to false alarm, our recent work (Raghavan and Polunchenko (2015)) establishes via extensive numerical studies that both the CUSUM chart and the SR procedure are second-order SADD-optimal. However, the design of detection thresholds to meet a certain ARL constraint (for either procedure) requires knowledge of both the pre-change and post-change parameters — an assumption that is difficult in many applications, especially in the post-change context. The focus of this work is thus on the study of different classes of mismatched detection procedures for detecting changes in autocorrelated data. We study the performance of: 1) a procedure that has knowledge of the pre- and post-change drifts leading to a mismatched test under the assumption of independent and identically distributed (i.i.d.) data that completely ignores the correlation coefficients in the pre- and post-change processes, and 2) a procedure that has knowledge of the pre-change parameters and the post-change drift leading to a mismatched test with a worst-case assumption for the post-change correlation coefficient.

References

Raghavan, V. and Polunchenko, A. S. (2015). Comparative performance analysis of Cumulative Sum chart and the Shiryaev-Roberts detection procedure for autocorrelated data. To be submitted.

Roberts, S. (1966). A comparison of some control chart procedures. Technometrics, 8(3):411–430.

Shiryaev, A. N. (1961). The problem of the most rapid detection of a disturbance in a stationary process. Soviet Math. Dokl., 2:795–799.

Shiryaev, A. N. (1963). On optimum methods in quickest detection problems. Theory of Probability and Its Applications, 8(1):22–46.