Non-partitioned e-detectors for nonparametric sequential change detection
arXiv:2607.28322
The paper proposes non‑partitioned e‑detectors for sequential change detection when both pre‑ and post‑change distributions are unknown, using aggregated e‑processes and showing asymptotically optimal detection delay.
Abstract
We study the problem of sequential change detection over a general class of probability distributions (), where both the pre-change and post-change distributions are unknown and belong to . We do not assume a pre-specified partition of into pre- and post-change families. We propose a general class of sequential change detectors obtained by aggregating point-null e-processes over possible changepoints and taking an infimum over candidate no-change distributions. The weights in the aggregation scheme determine whether they attain average run length (ARL) control and probability-of-false-alarm (PFA) control. Under suitable assumptions, we prove that our methods achieve first-order asymptotically optimal detection delay. Concrete examples include sub-Gaussian and bounded mean changes, Gaussian mean changes with unknown variance, as well as changes in Markov transition matrices.