The problem of quickest change detection is studied in the context of detecting an arbitrary unknown mean-shift in multiple independent Gaussian data streams. The James-Stein estimator is used in constructing detection schemes that exhibit strong detection performance both asymptotically and non-asymptotically. First, a James-Stein-based extension of the recently developed windowed CuSum test is introduced. Our results indicate that the proposed scheme constitutes a uniform improvement over its typical maximum likelihood variant. That is, the proposed James-Stein version achieves a smaller detection delay simultaneously for all possible post-change parameter values and every false alarm rate constraint, as long as the number of parallel data streams is greater than three. Additionally, an alternative detection procedure that utilizes the James-Stein estimator is shown to have asymptotic detection delay properties that compare favorably to existing tests. The second-order term of the asymptotic average detection delay is reduced in a predefined low-dimensional subspace of the parameter space, while second-order asymptotic minimaxity is preserved. The results are verified in simulations, where the proposed schemes are shown to achieve smaller detection delays compared to existing alternatives, especially when the number of data streams is large.

翻译：针对多个独立高斯数据流中任意未知均值偏移的检测问题，研究了快速变化检测方法。采用James-Stein估计器构建的检测方案在渐近与非渐近框架下均表现出优异的检测性能。首先，本文提出了基于James-Stein估计的窗口化CuSum检验扩展方法。结果表明，所提方案相对于经典的最大似然变体构成了系统性改进：当并行数据流数量大于三时，该James-Stein版本能在所有可能的变更后参数值与虚警率约束下同步实现更小的检测延迟。此外，基于James-Stein估计器的替代检测流程被证实具有优于现有检验的渐近检测延迟特性。在参数空间的预定义低维子空间中，渐近平均检测延迟的二阶项得到缩减，同时保持了二阶渐近极小化最优性。仿真结果验证了所提方案的有效性，表明其相较于现有替代方案能实现更小的检测延迟，尤其当数据流数量较大时优势更为显著。