A Robust Online Location–Scale Change-Point Detector under Dynamic Huber Contamination

Abstract

Online change-point detection must react rapidly to structural changes while controlling false alarms, a task that becomes substantially harder when streaming observations are subject to time-varying adversarial contamination and when the change may affect both location and scale. This paper develops an adaptive robust online location–scale detector under dynamic Huber contamination. The method uses two bounded score channels-a Huber location score and a centered winsorized quadratic scale score-and aggregates them over multiple window lengths and clipping constants. The theoretical model allows the contaminating marginal law to vary arbitrarily with time while retaining independence across observations; it does not assume a history-adaptive adversary. Bounded scores are used in this paper to give an anytime false-alarm bound for the known-baseline detector, and a deterministic perturbation proposition is established to translate high-probability location/scale estimation into an explicit score-centering allowance δₘ for the estimated-baseline detector, for which a false-alarm bound is given by an estimated-baseline false-alarm theorem. Local sensitivity can be used to give first-order separation between location and log-scale, and a high-probability detection-delay theorem is also given to make the adversarial detectability boundary explicit. Numerical studies are performed using 2,000 replications for each alternative and 5,000 null replications for calibration. Additional experiments, including matched-calibration, contamination-law, heavy-tail and operational-tuning studies, are also provided. For example, dynamically switching gross contamination at 10% was found to result in the proposed detector using a baseline allowance maintaining a pre-change false-alarm proportion of 0.056 on average, as opposed to 0.423 for a clean-calibrated unbounded rolling location–scale detector; post-change detection proportions were found to be 0.937 for location changes, 0.858 for joint changes, and a low 0.038 for pure scale changes – revealing a trade-off between robustness and efficiency. Sensitivity experiments were also performed, including the effect of underestimating the contamination envelope leading to high false-alarm rates, and that using larger reference samples for estimation of scale and joint changes results in materially better performance. Finally, the tuning of detectors is found to result in a loss of power through multiplicity, when using unnecessarily large grids. The proposed detector was found to signal the change in location on-line in 1906, as opposed to the unbounded location–scale comparator which signaled in 1913; and a single gross outlier, added to the data in 1895, was found to trigger the comparator immediately but to result in no alarm being triggered by the proposed detector. The proposed methodology therefore fills a significant methodological gap between the dynamic-contamination change-point model and that of joint online location–scale monitoring, and the assumptions made, the consequences of tuning, and the limitations of the proposed approach are all made explicit. Keywords: online change-point detection; Huber contamination; robust statistics; location-scale model; bounded scores; multiresolution monitoring; false-alarm control; detection delay.