Asymptotically optimal pointwise and minimax change-point detection for general stochastic models with a composite post-change hypothesis

JOURNAL OF MULTIVARIATE ANALYSIS

卷:174

Article

Pergamenchtchikov, Serguei^1,2  Tartakovsky, Alexander G.^3,4 

[1] Univ Rouen Normandie, Lab Math Raphael Salem, UMR 6085, CNRS, Mont St Aignan, France

[2] Natl Res Tomsk State Univ, Int Lab Stat Stochast Proc & Quantitat Finance, Tomsk, Russia

[3] Moscow Inst Phys & Technol, Space Informat Lab, Moscow, Russia

[4] AGT StatConsult, Los Angeles, CA USA

关键词: Asymptotic optimality;    Changepoint detection;    Composite post-change hypothesis;    Quickest detection;    Weighted Shiryaev-Roberts procedure;   

DOI  :  10.1016/j.jmva.2019.104541

来源: Elsevier

【 摘 要 】

A weighted Shiryaev-Roberts change detection procedure is shown to approximately minimize the expected delay to detection as well as higher moments of the detection delay among all change-point detection procedures with the given low maximal local probability of a false alarm within a window of a fixed length in pointwise and minimax settings for general non-i.i.d. data models and for the composite post-change hypothesis when the post-change parameter is unknown. We establish very general conditions for models under which the weighted Shiryaev-Roberts procedure is asymptotically optimal. These conditions are formulated in terms of the rate of convergence in the strong law of large numbers for the log-likelihood ratios between the change and no-change hypotheses, and we also provide sufficient conditions for a large class of ergodic Markov processes. Examples related to multivariate Markov models where these conditions hold are given. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free