Details
| Original language | English |
|---|---|
| Pages (from-to) | 1113-1137 |
| Number of pages | 25 |
| Journal | Biometrical journal |
| Volume | 58 |
| Issue number | 5 |
| Publication status | Published - 5 Sept 2016 |
| Externally published | Yes |
Abstract
In this paper, we propose a test procedure to detect change points of multidimensional autoregressive processes. The considered process differs from typical applied spatial autoregressive processes in that it is assumed to evolve from a predefined center into every dimension. Additionally, structural breaks in the process can occur at a certain distance from the predefined center. The main aim of this paper is to detect such spatial changes. In particular, we focus on shifts in the mean and the autoregressive parameter. The proposed test procedure is based on the likelihood-ratio approach. Eventually, the goodness-of-fit values of the estimators are compared for different shifts. Moreover, the empirical distribution of the test statistic of the likelihood-ratio test is obtained via Monte Carlo simulations. We show that the generalized Gumbel distribution seems to be a suitable limiting distribution of the proposed test statistic. Finally, we discuss the detection of lung cancer in computed tomography scans and illustrate the proposed test procedure.
Keywords
- Multidimensional, Simultaneous autoregressive model, Spatial autoregressive model, Spatial change point
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
Sustainable Development Goals
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In: Biometrical journal, Vol. 58, No. 5, 05.09.2016, p. 1113-1137.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Detection of spatial change points in the mean and covariances of multivariate simultaneous autoregressive models
AU - Otto, Philipp
AU - Schmid, Wolfgang
N1 - Publisher Copyright: © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
PY - 2016/9/5
Y1 - 2016/9/5
N2 - In this paper, we propose a test procedure to detect change points of multidimensional autoregressive processes. The considered process differs from typical applied spatial autoregressive processes in that it is assumed to evolve from a predefined center into every dimension. Additionally, structural breaks in the process can occur at a certain distance from the predefined center. The main aim of this paper is to detect such spatial changes. In particular, we focus on shifts in the mean and the autoregressive parameter. The proposed test procedure is based on the likelihood-ratio approach. Eventually, the goodness-of-fit values of the estimators are compared for different shifts. Moreover, the empirical distribution of the test statistic of the likelihood-ratio test is obtained via Monte Carlo simulations. We show that the generalized Gumbel distribution seems to be a suitable limiting distribution of the proposed test statistic. Finally, we discuss the detection of lung cancer in computed tomography scans and illustrate the proposed test procedure.
AB - In this paper, we propose a test procedure to detect change points of multidimensional autoregressive processes. The considered process differs from typical applied spatial autoregressive processes in that it is assumed to evolve from a predefined center into every dimension. Additionally, structural breaks in the process can occur at a certain distance from the predefined center. The main aim of this paper is to detect such spatial changes. In particular, we focus on shifts in the mean and the autoregressive parameter. The proposed test procedure is based on the likelihood-ratio approach. Eventually, the goodness-of-fit values of the estimators are compared for different shifts. Moreover, the empirical distribution of the test statistic of the likelihood-ratio test is obtained via Monte Carlo simulations. We show that the generalized Gumbel distribution seems to be a suitable limiting distribution of the proposed test statistic. Finally, we discuss the detection of lung cancer in computed tomography scans and illustrate the proposed test procedure.
KW - Multidimensional
KW - Simultaneous autoregressive model
KW - Spatial autoregressive model
KW - Spatial change point
UR - http://www.scopus.com/inward/record.url?scp=85027929427&partnerID=8YFLogxK
U2 - 10.1002/bimj.201500148
DO - 10.1002/bimj.201500148
M3 - Article
VL - 58
SP - 1113
EP - 1137
JO - Biometrical journal
JF - Biometrical journal
SN - 0323-3847
IS - 5
ER -