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arXiv · 2607.28322

Non-partitioned e-detectors for nonparametric sequential change detection

Aytijhya Saha·Aaditya Ramdas
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Abstract

We study the problem of sequential change detection over a general class of probability distributions ($\mathcal P$), where both the pre-change and post-change distributions are unknown and belong to $\mathcal P$. We do not assume a pre-specified partition of $\mathcal P$ 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.

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Aytijhya Saha, Aaditya Ramdas. 2026-07-30. Non-partitioned e-detectors for nonparametric sequential change detection. https://arxiv.org/abs/2607.28322

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