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The $K$ sample problem for high-dimensional vector time series is studied,especially focusing on sensor data streams, in order to analyze the secondmoment structure and detect changes across samples and/or across variablescumulated sum (CUSUM) statistics of bilinear forms of the sample covariancematrix. 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 $d$-dimensionaldata as well as $K$ locations where $d$ sensors emit univariate data. Unequalsample sizes are considered as arising when the sampling rate of the sensorsdiffers. We provide large sample approximations and two related change-pointstatistics, a sums of squares and a pooled variance statistic. The resultingprocedures are investigated by simulations and illustrated by analyzing a realdata set.

Detecting Changes in the Second Moment Structure of High-Dimensional Sensor-Type Data in a $K$-Sample Setting