Non-partitioned e-detectors for nonparametric sequential change detection

2026-07-30

AI Summary

This work addresses the problem of real-time, nonparametric change-point detection in sequential data where both pre- and post-change distributions are unknown and no prior partitioning of distribution families is assumed. The authors propose a general detection framework based on e-process aggregation and optimization over the infimum under candidate no-change distributions. This approach uniformly controls both the average run length (ARL) and the probability of false alarm (PFA) without requiring prespecified distributional assumptions, while achieving first-order asymptotically optimal detection delay. By integrating nonparametric hypothesis testing with sequential analysis, the method demonstrates first-order asymptotic optimality across several canonical settings, including sub-Gaussian observations, bounded-mean processes, Gaussian mean shifts with unknown variance, and changes in Markov transition matrices.

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.

Problem

• sequential change detection
• nonparametric
• unknown distributions
• e-processes
• change point

Innovation

• e-detectors
• sequential change detection
• nonparametric
• asymptotic optimality
• e-processes