Numerical Comparison of CUSUM and Shiryaev–Roberts Procedures for Detecting Changes in Distributions

By George V. Moustakides, Aleksey S. Polunchenko, Alexander G. Tartakovsky. 2009

52 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b10f8772e6308e1d8c9c4c9932d1f858803d7422

Citations in the corpus

• On optimality of the Shiryaev-Roberts procedure for detecting a change in distribution (2009, unknown): “Moustakides, Polunchenko, and Tartakovsky (2010, 2009) used the Markov property of the SR-r statistic (9) to obtain the following integral equations for performance metrics φ(r) = 1 + ∫ A 0 φ(x) ∂ ∂x F∞ ( x 1 + r ) dx(15) δ0(r) = 1 + ∫ A 0 δ0(x) ∂ ∂x F0 ( x 1 + r ) dx(16) δν(r) = ∫ A 0 δν−1(x) ∂ ∂x…”