Detecting changes in the mean of spatial random fields on a regular grid

Abstract

We propose statistical procedures for detecting changes in the mean of spatial random fields observed on regular grids. The proposed framework provides a general approach to change detection in spatial processes. Extending a block-based method originally developed for time series, we introduce two test statistics, one based on Gini's mean difference and a novel variance-based variant. Under mild moment conditions, we derive asymptotic normality of the variance-based statistic and prove its consistency against almost all non-constant mean functions (in a sense of positive Lebesgue measure). To accommodate spatial dependence, we modify our procedures for M-dependent data and we further develop a de-correlation algorithm based on estimated autocovariances. Monte Carlo simulations demonstrate that the tests maintain appropriate size and power for both independent and dependent data. In an application to satellite images, especially our variance-based test reliably detects regions undergoing deforestation.