A change-point problem for $m$-dependent multivariate random field

Abstract

In this paper, we consider a change-point problem for a centered, stationary and $m$-dependent multivariate random field. Under the distribution free assumption, a change-point test using CUSUM statistic is proposed to detect anomalies within a multidimensional random field, controlling the false positive rate as well as the Family-Wise Error in the multiple hypotheses testing context.