A change-point–based control chart for detecting sparse mean changes in high-dimensional heteroscedastic data

Because of the “curse of dimensionality,” high-dimensional processes present challenges to traditional multivariate statistical process monitoring (SPM) techniques. In addition, the unknown underlying distribution of and complicated dependency among variables such as heteroscedasticity increase the uncertainty of estimated parameters and decrease the effectiveness of control charts. In addition, the requirement of sufficient reference samples limits the application of traditional charts in high-dimension, low-sample-size scenarios (small n, large p). More difficulties appear when detecting and diagnosing abnormal behaviors caused by a small set of variables (i.e., sparse changes). In this article, we propose two change-point–based control charts to detect sparse shifts in the mean vector of high-dimensional heteroscedastic processes. Our proposed methods can start monitoring when the number of observations is a lot smaller than the dimensionality. The simulation results show that the proposed methods are robust to nonnormality and heteroscedasticity. Two real data examples are used to illustrate the effectiveness of the proposed control charts in high-dimensional applications. The R codes are provided online.

受维数灾难（curse of dimensionality）影响，高维过程给传统多元统计过程监控（multivariate statistical process monitoring, SPM）技术带来了挑战。此外，变量未知的潜在分布与复杂依赖关系（如异方差性（heteroscedasticity））会增大估计参数的不确定性，降低控制图（control charts）的监控效果。同时，传统控制图对充足参考样本的要求限制了其在高维低样本量场景（small n, large p）中的应用。若需检测与诊断由少量变量引发的异常行为（即稀疏变化（sparse changes）），则会面临更多难题。本文提出两种基于变点（change-point）的控制图，用于检测高维异方差过程均值向量（mean vector）中的稀疏偏移（sparse shifts）。所提方法可在观测数远小于过程维数的情况下启动监控。仿真结果表明，所提方法对非正态性（nonnormality）与异方差性具有鲁棒性。本文通过两个实际数据案例，验证了所提控制图在高维应用场景中的有效性。相关R代码（R codes）已在线公开。