Abstract 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 are observed over a time span 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 sum of squares and a pooled variance statistic. The resulting procedures are investigated by simulations and illustrated by analyzing a real data set.

中文翻译：

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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

摘要 研究了高维向量时间序列的 K 样本问题，特别关注传感器数据流，以分析二阶矩结构并检测跨样本和/或跨变量累积和 (CUSUM) 统计的双线性形式的变化。样本协方差矩阵。在该模型中，在一个时间跨度内观察到 K 个独立向量时间序列，这可能对应于产生 d 维数据的 K 个传感器（位置）以及 d 个传感器发出单变量数据的 K 个位置。当传感器的采样率不同时，会认为样本大小不等。我们提供大样本近似值和两个相关的变化点统计量，一个平方和和一个合并方差统计量。由此产生的程序通过模拟进行研究，并通过分析真实数据集来说明。