A computationally efficient approach on detecting star-shaped change boundaries in random fields with heavy-tailed distributions

Tsung-Lin Cheng and Jheng-Ting Wang

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 169, issue C, 16-25

Abstract: One of the difficulties on detecting the change boundary in a random field is the implementation, especially when the random disturbances have heavy-tailed distributions. Thank to the gearing of the computer technology, a huge amount of image data can be retrieved in real time. In the cases when a change boundary is star-shaped (e.g. circular or elliptical) and divides an area into two regions with different distributions, some well-known methods dealing with random fields in Cartesian coordinate cannot be directly applied to detect the boundary computationally efficiently. In particular, when the distribution of the underlying region is heavy-tailed, some moment-based CUSUM estimators are not viable. In this paper, we propose a computationally efficient method to detect the star-shaped change boundaries in a stationary random field. Instead of Cartesian coordinate, we consider the random fields to be polar-coordinated indexed. Compared with the existed approaches, our simulation studies show that our method can outperform especially for change-in-variance problems in the heavy-tailed distributional models.

Keywords: Star-shaped change boundary; CUSUM; Random fields; Heavy-tailed distribution (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:169:y:2020:i:c:p:16-25

DOI: 10.1016/j.matcom.2019.10.008

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