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Kullback-Leibler Approach to CUSUM Quickest Detection Rule for Markovian Time Series

机译：马尔可夫时间序列CUSUM最快检测规则的Kullback-Leibler方法

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摘要

Optimality properties of decision procedures are studied for the quickest detection of a change-point of parameters in autoregressive and other Markov type sequences. The limit of the normalized conditional log-likelihood ratios is shown to exist for Markov chains satisfying the ergodic theorem of information theory. Then closed-form expressions for this limit are derived by making use of the time average rate of Kullback-Leibler divergence. The good properties of the detection procedures based on a sequential analysis approach are proven to hold thanks to geometric ergodicity properties of the observation processes. In particular, the window-limited CUSUM rule is shown to be optimal for detecting the disruption point in autoregressive models. Sparre Andersen models are specifically studied.
机译：研究了决策程序的最优性质，以最快地检测自回归和其他马尔可夫类型序列中的参数变化点。对于满足信息论遍历定理的马尔可夫链，存在归一化条件对数似然比的极限。然后，利用Kullback-Leibler发散的时间平均速率，得出该极限的封闭形式的表达式。事实证明，基于顺序分析方法的检测程序具有良好的性能，这要归功于观测过程的几何遍历性。特别地，显示了窗口受限的CUSUM规则对于检测自回归模型中的破坏点是最佳的。专门研究了Sparre Andersen模型。

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