Abstract

We present an efficient score statistic, called the ${\mathsf{S}}^3\mathsf{T}$ statistic, to detect the emergence of a spatially and temporally correlated signal from either fixed-sample or sequential data. The signal may cause a mean shift and/or a change in the covariance structure. The score statistic can capture both the spatial and temporal structures of the change and hence is particularly powerful in detecting weak signals. The score statistic is computationally efficient and statistically powerful. Our main theoretical contribution is accurate analytical approximations to the false alarm rate of the detection procedures, which can be used to calibrate the threshold analytically. Numerical experiments on simulated and real data, as well as a case study of water quality monitoring using sensor networks, demonstrate the good performance of our procedure.

摘要

我们提供了一个有效的得分统计数据，称为 ${\mathsf{小号}}^3\mathsf{Ť}$统计数据，以从固定样本或顺序数据中检测时空相关信号的出现。该信号可能导致协方差结构的均值漂移和/或变化。得分统计可以捕获变化的空间和时间结构，因此在检测微弱信号方面特别强大。分数统计量在计算上有效且在统计上强大。我们的主要理论贡献是对检测程序的误报率进行精确的分析近似，可用于分析校准阈值。在模拟和真实数据上进行的数值实验以及使用传感器网络进行水质监测的案例研究证明了我们程序的良好性能。