Numerical Comparison of Cusum and Shiryaev-Roberts Procedures for Detecting Changes in Distributions

Abstract

The CUSUM procedure is known to be optimal for detecting a change in distribution under a minimax scenario, whereas the Shiryaev-Roberts procedure is optimal for detecting a change that occurs at a distant time horizon. As a simpler alternative to the conventional Monte Carlo approach, we propose a numerical method for the systematic comparison of the two detection schemes in both settings, i.e., minimax and for detecting changes that occur in the distant future. Our goal is accomplished by deriving a set of exact integral equations for the performance metrics, which are then solved numerically. We present detailed numerical results for the problem of detecting a change in the mean of a Gaussian sequence, which show that the difference between the two procedures is significant only when detecting small changes.

21 pages, 8 figures, to appear in Communications in Statistics - Theory and Methods

References in corpus (2)

• On Optimality Properties of the Shiryaev-Roberts Procedure
• Sequential change detection revisited

Cited by in corpus (5)

• On optimality of the Shiryaev-Roberts procedure for detecting a change in distribution
• The Steady-State Behavior of Multivariate Exponentially Weighted Moving Average Control Charts
• On Control Charts for Monitoring the Variance of a Time Series
• Max-Type and Sum-Type Procedures for Online Change-Point Detection in the Mean of High-Dimensional Data
• An Accurate Method for Determining the Pre-Change Run-Length Distribution of the Generalized Shiryaev--Roberts Detection Procedure