Detection of spatial change points in the mean and covariances of multivariate simultaneous autoregressive models

authored by

Philipp Otto, Wolfgang Schmid

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.

External Organisation(s)

European University Viadrina in Frankfurt (Oder)

Type

Article

Journal

Biometrical journal

Volume

58

Pages

1113-1137

No. of pages

25

ISSN

0323-3847

Publication date

05.09.2016

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Statistics and Probability, Statistics, Probability and Uncertainty

Sustainable Development Goals

SDG 3 - Good Health and Well-being

Electronic version(s)

https://doi.org/10.1002/bimj.201500148 (Access: Closed)