Asymptotically Optimal Pointwise and Minimax Change-point Detection for General Stochastic Models With a Composite Post-Change Hypothesis

Serguei Pergamenchtchikov; Alexander G. Tartakovsky

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arXiv · 1807.09613

Asymptotically Optimal Pointwise and Minimax Change-point Detection for General Stochastic Models With a Composite Post-Change Hypothesis

Serguei Pergamenchtchikov·Alexander G. Tartakovsky

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Abstract

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 the 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, where these conditions hold, are given.

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Serguei Pergamenchtchikov, Alexander G. Tartakovsky. 2018-07-24. Asymptotically Optimal Pointwise and Minimax Change-point Detection for General Stochastic Models With a Composite Post-Change Hypothesis. https://arxiv.org/abs/1807.09613

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