具有稀疏均值位移的高维过程的相位I变点法

Wenpo Huang, L. Shu, Yanting Li, Luyao Wang
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引用次数: 1

摘要

尽管多元过程的第一阶段分析已被广泛讨论,但对高维过程的第一阶段监测技术的讨论仍然有限。在高维应用中,通常观察到大量的组件,但只有有限数量的组件同时发生变化。在实践中,移位的分量通常是稀疏的,并且是先验未知的。基于此,本文研究了未知位移稀疏度下高维过程均值向量的第一阶段监测。所提出的监测方案的基本思想是首先采用错误发现率过程来估计平均位移的稀疏程度,然后根据所有可能移动方向上的方向似然比统计量的最大值来监测平均变化。基于大量仿真的比较结果支持所提出的监测方案。最后通过一个实例说明了该监控方案的实现。
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A phase I change‐point method for high‐dimensional process with sparse mean shifts
Although Phase I analysis of multivariate processes has been extensively discussed, the discussion on techniques for Phase I monitoring of high‐dimensional processes is still limited. In high‐dimensional applications, it is common to observe that a large number of components but only a limited number of them change at the same time. The shifted components are often sparse and unknown a priori in practice. Motivated by this, this article studies Phase I monitoring of high‐dimensional process mean vectors under an unknown sparsity level of shifts. The basic idea of the proposed monitoring scheme is to first employ the false discovery rate procedure to estimate the sparsity level of mean shifts, and then to monitor the mean changes based on the maximum of the directional likelihood ratio statistics over all the possible shift directions. The comparison results based on extensive simulations favor the proposed monitoring scheme. A real example is presented to illustrate the implementation of the new monitoring scheme.
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