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Statistica Sinica 32 (2022), 1961-1981

INFERENCE FOR STRUCTURAL BREAKS
IN SPATIAL MODELS

Ngai Hang Chan1, Rongmao Zhang2,3 and Chun Yip Yau1

1The Chinese University of Hong Kong,
2Zhejiang University and 3Zhejiang University City College

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.

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