Abstract: Testing for structural changes in spatial trends constitutes an important issue in many biomedical and geophysical applications. In this paper, a novel statistic based on a discrepancy measure over small blocks is proposed. This measure can be used not only to construct tests for structural breaks, but also to identify the change-boundaries of the breaks. The asymptotic properties and limit distributions of the proposed tests are also established. To derive the asymptotics, the notion of spatial physical dependence is adopted to account for the spatial dependence structure. A bootstrap procedure is applied to the proposed statistic to handle the asymptotic variance of the limit distribution. The method is illustrated by means of simulations and a data analysis.

Key words and phrases: Change-boundaries, discrepancy measure, inference, non-stationary processes, spatial trends.