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Kullback-Leibler Approach to CUSUM Quickest Detection Rule for Markovian Time Series
| Content Provider | Scilit |
|---|---|
| Author | Girardin, Valérie Konev, Victor Pergamenchtchikov, Serguei |
| Copyright Year | 2018 |
| Description | 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. |
| Related Links | https://hal.archives-ouvertes.fr/hal-02334914/file/GKPrevision_HAL.pdf |
| Ending Page | 341 |
| Page Count | 20 |
| Starting Page | 322 |
| ISSN | 07474946 |
| e-ISSN | 15324176 |
| DOI | 10.1080/07474946.2018.1548846 |
| Journal | Sequential Analysis |
| Issue Number | 3 |
| Volume Number | 37 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2018-07-03 |
| Access Restriction | Open |
| Subject Keyword | Journal: Sequential Analysis Statistics and Probability Change-point Detection Cusum Detection Procedure Ergodic Theorem of Information Theory Kullback-leibler Divergence Relative Entropy Sequential Detection Sparre Andersen Models 62l10 62l15 60g40 60j10 62b10 94a17 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Statistics and Probability Modeling and Simulation |
