在$K$样本设置中检测高维传感器类型数据的二阶矩结构的变化
Detecting Changes in the Second Moment Structure of High-Dimensional Sensor-Type Data in a $K$-Sample Setting
摘要：
研究了高维向量时间序列的$K$样本问题，特别是针对传感器数据流，以分析二阶矩结构并检测样本协方差阵双线性型的跨样本和/或跨变量累积和统计量的变化.在该模型中，在时间跨度$ [0,T] $上观察$K$独立向量时间序列$\mathbf{Y}_{T,1},\dots,\mathbf{Y}_{T,K}$，该时间跨度可以对应于产生$d$维度数据的$K$传感器（位置）以及$d$传感器发出单变量数据的$K$位置。不相等的样本量被认为是当传感器的采样率不同时产生的。我们提供了大样本近似和两个相关的变点统计，平方和和合并方差统计。由此产生的程序进行了研究，通过模拟和分析一个真实的数据集。
英文摘要：
The $K$ sample problem for high-dimensional vector time series is studied, especially focusing on sensor data streams, in order to analyze the second moment structure and detect changes across samples and/or across variables cumulated sum (CUSUM) statistics of bilinear forms of the sample covariance matrix. In this model $K$ independent vector time series $\mathbf{Y}_{T,1},\dots,\mathbf{Y}_{T,K}$ are observed over a time span $ [0,T] $, which may correspond to $K$ sensors (locations) yielding $d$-dimensional data as well as $K$ locations where $d$ sensors emit univariate data. Unequal sample sizes are considered as arising when the sampling rate of the sensors differs. We provide large sample approximations and two related change-point statistics, a sums of squares and a pooled variance statistic. The resulting procedures are investigated by simulations and illustrated by analyzing a real data set.
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