Control charts for multivariate spatial autoregressive models

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• 作者：Robert Garthoff ; Philipp Otto
• 关键词：Multivariate CUSUM charts ; Multivariate EWMA charts ; Spatial autoregressive model
• 刊名：AStA Advances in Statistical Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：101
• 期：1
• 页码：67-94
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics, general; Statistics for Business/Economics/Mathematical Finance/Insurance; Probability Theory and Stochastic Processes; Econometrics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1863-818X
• 卷排序：101

文摘

This paper deals with spatial detection of changes in model parameters of spatial autoregressive processes. The respective sequential testing problems are formulated. Moreover, we introduce characteristic quantities to monitor means or covariances of multivariate spatial autoregressive processes. Additionally, we also take into account the simultaneous surveillance of the mean vector and the covariance matrix. The aim is to apply control charts, important tools of sequential analysis, to these quantities. The considered control procedures are based on either cumulative sums or exponential smoothing. Further, we illustrate the methodology of statistical process control studying the spectrum of additive colors in a satellite photograph. Via simulation studies, the proposed control procedures are calibrated for a predefined average run length. In addition, we compare the performance of the control procedures considering the out-of-control situation. Eventually, the control charts are applied, and the signals of the different schemes are visualized. The final results are critically discussed.