高维异方差数据稀疏变化的变点控制图
A Change-Point Based Control Chart for Detecting Sparse Changes in High-Dimensional Heteroscedastic Data
摘要：
由于高维过程的维数灾难性，传统的多变量统计过程监控（SPM）技术提出了挑战。此外，未知的潜在分布和变量之间的复杂相关性，如异方差，增加了估计参数的不确定性，降低了控制图的有效性。此外，对足够参考样本的要求限制了传统图表在高维低样本量场景（小n，大p）中的应用。在检测和诊断由一小组变量引起的异常行为时出现了更多的困难，即，稀疏的变化。在这篇文章中，我们提出了一个基于变点的控制图来检测高维异方差过程的均值向量的稀疏移位。我们提出的方法可以在观测值的数量比维数小得多时开始监测。仿真结果表明了该方法对非正态性和异方差的鲁棒性。一个实际数据的例子被用来说明所提出的控制图在高维应用的有效性。在线提供补充材料和代码。
英文摘要：
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 and complicated dependency among variables such as heteroscedasticity increase 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 in detecting and diagnosing abnormal behaviors that are caused by a small set of variables, i.e., sparse changes. In this article, we propose a changepoint based control chart to detect sparse shifts in the mean vector of high-dimensional heteroscedastic processes. Our proposed method can start monitoring when the number of observations is a lot smaller than the dimensionality. The simulation results show its robustness to nonnormality and heteroscedasticity. A real data example is used to illustrate the effectiveness of the proposed control chart in high-dimensional applications. Supplementary material and code are provided online.
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