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 -