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

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.