title: Detection of spatial change points in the mean and covariances of multivariate simultaneous autoregressive models.
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.
authors.affiliation: Department of Statistics, European University Viadrina, Große Scharrnstraße 59, 15230 Frankfurt (Oder), Germany. potto@europa-uni.de.
authors.forename: Philipp
authors.initials: P
authors.lastname: Otto
authors.affiliation: Department of Statistics, European University Viadrina, Große Scharrnstraße 59, 15230 Frankfurt (Oder), Germany.
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Schmid
mesh_terms: D003198:Computer Simulation; D006801:Humans; D008175:Lung Neoplasms / Q000000981:diagnostic imaging; D008962:Models, Theoretical; D009010:Monte Carlo Method; D014057:Tomography, X-Ray Computed
keywords: Multidimensional; Simultaneous autoregressive model; Spatial autoregressive model; Spatial change point