Asymptotically Optimal Pointwise and Minimax Change-point Detection for General Stochastic Models With a Composite Post-Change Hypothesis
| Autor: | Pergamenchtchikov, Serguei, Tartakovsky, Alexander G. |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Journal of Multivariate Analysis, 2019 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 21 pages. arXiv admin note: text overlap with arXiv:1510.02903 |
| Databáze: | arXiv |
| Externí odkaz: |
|