Whittle estimation based on the extremal spectral density of a heavy-tailed random field
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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.
Originalsprog | Engelsk |
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Tidsskrift | Stochastic Processes and Their Applications |
Vol/bind | 155 |
Sider (fra-til) | 232-267 |
ISSN | 0304-4149 |
DOI | |
Status | Udgivet - 2023 |
Bibliografisk note
Funding Information:
Ewa Damek’s research is partly supported by the NCN, Poland grant 2019/33/B/ST1/00207 . Thomas Mikosch’s research is partly supported by Danmarks Frie Forskningsfond, Denmark Grant No. 9040-00086B . Yuwei Zhao’s research is partly supported by the NSFC, China Grant No. 11971115 and No. 1181086 .
Publisher Copyright:
© 2022 Elsevier B.V.
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