Whittle estimation based on the extremal spectral density of a heavy-tailed random field
Statistics Theory
2022-11-08 v1 Probability
Methodology
Statistics Theory
Abstract
We consider a strictly stationary random field on the two-dimensional integer lattice with regularly varying marginal and finite-dimensional distributions. Exploiting the regular variation, we define the spatial extremogram which takes into account only the largest values in the random field. This extremogram is a spatial autocovariance function. We define the corresponding extremal spectral density and its estimator, the extremal periodogram. Based on the extremal periodogram, we consider the Whittle estimator for suitable classes of parametric random fields including the Brown-Resnick random field and regularly varying max-moving averages.
Keywords
Cite
@article{arxiv.2211.03260,
title = {Whittle estimation based on the extremal spectral density of a heavy-tailed random field},
author = {Ewa Damek and Thomas Mikosch and Yuwei Zhao and Jacek Zienkiewicz},
journal= {arXiv preprint arXiv:2211.03260},
year = {2022}
}