Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

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 related to multivariate Markov models where these

conditions hold are given.

This is a joint work with Alexander G. Tartakovsky (Moscow Institute of Physics and Technology).