Abstract: Non-stationary spatial phenomena are common in various fields such as climate and medical image processing. While many methods examine non-stationary spatial covariance structures, more methods are needed for detecting sudden trend breaks in spatial data. Based on the maximal value of the neighboring discrepancy measurement in the sample space, this paper presents an extreme-value test statistic to detect trend breaks. A simulation-based algorithm is developed to detect breaks in spatial trends at various locations, from which the shape of changing boundaries can be revealed. A simulation study reveals that the test is very effective in detecting structural breaks, especially when they appear at the boundary of the sampling region. Analyses of Australian rainfall and lung tumor data demonstrate the accuracy and wide applicability of the proposed method.

Key words and phrases: Change boundary, extreme value theory, inference, long-run variance.