Whittle estimation based on the extremal spectral density of a heavy-tailed random field
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Whittle estimation based on the extremal spectral density of a heavy-tailed random field. / Damek, Ewa; Mikosch, Thomas; Zhao, Yuwei; Zienkiewicz, Jacek.
In: Stochastic Processes and Their Applications, Vol. 155, 2023, p. 232-267.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Whittle estimation based on the extremal spectral density of a heavy-tailed random field
AU - Damek, Ewa
AU - Mikosch, Thomas
AU - Zhao, Yuwei
AU - Zienkiewicz, Jacek
N1 - Publisher Copyright: © 2022 Elsevier B.V.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - Brown-Resnick random field
KW - Extreme value theory
KW - Max-moving averages
KW - Spectral analysis
KW - Whittle estimation
U2 - 10.1016/j.spa.2022.10.004
DO - 10.1016/j.spa.2022.10.004
M3 - Journal article
AN - SCOPUS:85140929937
VL - 155
SP - 232
EP - 267
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
ER -
ID: 371272954