Asymptotic properties of maximum composite likelihood estimators for max-stable Brown-Resnick random fields over a fixed-domain

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Autori principali: Chenavier, Nicolas, Robert, Christian Y.
Natura: Preprint
Pubblicazione: 2025
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author Chenavier, Nicolas
Robert, Christian Y.
author_facet Chenavier, Nicolas
Robert, Christian Y.
contents Likelihood inference for max-stable random fields is in general impossible because their finite-dimensional probability density functions are unknown or cannot be computed efficiently. The weighted composite likelihood approach that utilizes lower dimensional marginal likelihoods (typically pairs or triples of sites that are not too distant) is rather favored. In this paper, we consider the family of spatial max-stable Brown-Resnick random fields associated with isotropic fractional Brownian fields. We assume that the sites are given by only one realization of a homogeneous Poisson point process restricted to $\mathbf{C}=(-1/2,1/2]^{2}$ and that the random field is observed at these sites. As the intensity increases, we study the asymptotic properties of the composite likelihood estimators of the scale and Hurst parameters of the fractional Brownian fields using different weighting strategies: we exclude either pairs that are not edges of the Delaunay triangulation or triples that are not vertices of triangles.
format Preprint
id arxiv_https___arxiv_org_abs_2503_05880
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Asymptotic properties of maximum composite likelihood estimators for max-stable Brown-Resnick random fields over a fixed-domain
Chenavier, Nicolas
Robert, Christian Y.
Statistics Theory
Likelihood inference for max-stable random fields is in general impossible because their finite-dimensional probability density functions are unknown or cannot be computed efficiently. The weighted composite likelihood approach that utilizes lower dimensional marginal likelihoods (typically pairs or triples of sites that are not too distant) is rather favored. In this paper, we consider the family of spatial max-stable Brown-Resnick random fields associated with isotropic fractional Brownian fields. We assume that the sites are given by only one realization of a homogeneous Poisson point process restricted to $\mathbf{C}=(-1/2,1/2]^{2}$ and that the random field is observed at these sites. As the intensity increases, we study the asymptotic properties of the composite likelihood estimators of the scale and Hurst parameters of the fractional Brownian fields using different weighting strategies: we exclude either pairs that are not edges of the Delaunay triangulation or triples that are not vertices of triangles.
title Asymptotic properties of maximum composite likelihood estimators for max-stable Brown-Resnick random fields over a fixed-domain
topic Statistics Theory
url https://arxiv.org/abs/2503.05880