Details
| Original language | English |
|---|---|
| Pages (from-to) | 67-94 |
| Number of pages | 28 |
| Journal | AStA Advances in Statistical Analysis |
| Volume | 101 |
| Issue number | 1 |
| Early online date | 26 Jul 2016 |
| Publication status | Published - Jan 2017 |
| Externally published | Yes |
Abstract
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.
Keywords
- Multivariate CUSUM charts, Multivariate EWMA charts, Spatial autoregressive model
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Modelling and Simulation
- Social Sciences(all)
- Social Sciences (miscellaneous)
- Economics, Econometrics and Finance(all)
- Economics and Econometrics
- Mathematics(all)
- Applied Mathematics
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In: AStA Advances in Statistical Analysis, Vol. 101, No. 1, 01.2017, p. 67-94.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Control charts for multivariate spatial autoregressive models
AU - Garthoff, Robert
AU - Otto, Philipp
N1 - Publisher Copyright: © 2016, Springer-Verlag Berlin Heidelberg.
PY - 2017/1
Y1 - 2017/1
N2 - 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.
AB - 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.
KW - Multivariate CUSUM charts
KW - Multivariate EWMA charts
KW - Spatial autoregressive model
UR - http://www.scopus.com/inward/record.url?scp=84979687763&partnerID=8YFLogxK
U2 - 10.1007/s10182-016-0276-x
DO - 10.1007/s10182-016-0276-x
M3 - Article
VL - 101
SP - 67
EP - 94
JO - AStA Advances in Statistical Analysis
JF - AStA Advances in Statistical Analysis
SN - 1863-8171
IS - 1
ER -