Detecting changes in the second moment structure of high-dimensional sensor-type data in a K-sample setting. Issue 3 (2nd July 2020) - Mause, Nils; Steland, Ansgar
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 Y T, 1, …, 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 sum of squares and a pooled variance statistic. The resulting procedures are investigated by simulations and illustrated by analyzing a real data set.