Detecting changes in the second moment structure of high-dimensional sensor-type data in a K-sample setting. Issue 3 (2nd July 2020)

• Record Type: Journal Article
• Authors: Mause, Nils; Steland, Ansgar
• Is Part Of: Sequential analysis. Volume 39:Issue 3(2020)
• Page Start: 336
• Page End: 366
• Publication Date: 2020-07-02
• Subjects: Brownian motion -- change points -- data science -- linear process -- multivariate analysis -- sensor monitoring -- strong approximation -- time series; 62R07 -- 60F17 -- 62L10 -- 62P30; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2020.1823192
• Languages: English
• ISSNs: 0747-4946

Abstract

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.