Quickest change-point detection in time series with unknown distributions S. M. Pergamenshchikov, A. G. Tartakovsky
Material type: ArticleSubject(s): асимптотическая оптимальность | Ширяева-Робертса процедура | временные ряды | марковские моделиGenre/Form: статьи в сборниках Online resources: Click here to access online In: 31st European modeling and simulation symposium (EMSS 2019) : held at the International Multidisciplinary Modeling and Simulation Multiconference (I3M 2019), Lisbon, Portugal, 18-20 September 2019 P. 29-33Abstract: We consider a problem of sequential detection of changes in general time series, in which case the observations are dependent and non-identically distributed, e.g., follow Markov, hidden Markov or even more general stochastic models. It is assumed that the pre-change model is completely known, but the post-change model contains an unknown (possibly vector) parameter. Imposing a distribution on the unknown post-change parameter, we design a mixture Shiryaev-Roberts change detection procedure in such a way that the maximal local probability of a false alarm (MLPFA) in a prespecified time window does not exceed a given level and show that this procedure is nearly optimal as the MLPFA goes to zero in the sense of minimizing the expected delay to detection uniformly over all points of change under very general conditions. 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 “nochange” hypotheses. An example related to a multivariate Markov model where these conditions hold is given.Библиогр.: с. 32-33
We consider a problem of sequential detection of changes in general time series, in which case the observations are dependent and non-identically distributed, e.g., follow Markov, hidden Markov or even more general stochastic models. It is assumed that the pre-change model is completely known, but the post-change model contains an unknown (possibly vector) parameter. Imposing a distribution on the unknown post-change parameter, we design a mixture Shiryaev-Roberts change detection procedure in such a way that the maximal local probability of a false alarm (MLPFA) in a prespecified time window does not exceed a given level and show that this procedure is nearly optimal as the MLPFA goes to zero in the sense of minimizing the expected delay to detection uniformly over all points of change under very general conditions. 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 “nochange” hypotheses. An example related to a multivariate Markov model where these conditions hold is given.
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