论文标题
在$ k $样本设置中检测高维传感器型数据的第二刻结构的变化
Detecting Changes in the Second Moment Structure of High-Dimensional Sensor-Type Data in a $K$-Sample Setting
论文作者
论文摘要
研究了$ K $样本的样本问题，用于研究高维矢量时间序列，尤其是专注于传感器数据流，以分析第二矩结构并检测到样品和/或变量之间的变化累积总和（cusum）样品协方差矩阵的双线性形式的统计。 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.当传感器的采样速率不同时，将样本量视为不等的样本量。我们提供大型样本近似值和两个相关的更改点统计数据，一个正方和汇总差异统计量。通过模拟研究了结果程序，并通过分析真实数据集进行了说明。
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.
