Asymptotically Optimal Pointwise and Minimax Changepoint Detection for General Stochastic Models With a Composite Post-Change Hypothesis
Salle de séminaires, M.0.1
LMRS, Univ. de Rouen
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).