Maxima of a triangular array of multivariate Gaussian sequence

Hashorva, Enkelejd; Peng, Liang; Weng, Zhichao

doi:10.1016/j.spl.2015.04.007

Cited by 5 publications

(1 citation statement)

References 12 publications

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“…Using analogues of conditions of [15], which allow for strong local dependence among variables while keeping their asymptotic independence, [13] generalized the results of [15] and [14] to multivariate stationary Gaussian triangular arrays. The limiting distribution of the normalized maxima for Gaussian random vectors was derived, and [14] established the limit law for the bivariate stationary Gaussian triangular arrays.…”

Section: Introductionmentioning

confidence: 99%

Point process of clusters for a stationary Gaussian random field on a lattice

Yingyin Lu,

Jinhui Guo

2023

PMS

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It is well established that the normalized exceedances resulting from a standard stationary Gaussian triangular array at high levels follow a Poisson process under the Berman condition. To model frequent cluster phenomena, we consider the asymptotic distribution of the point process of clusters for a Gaussian random field on a lattice. Our analysis demonstrates that the point process of clusters also converges to a Poisson process in distribution, provided that the correlations of the Gaussian random field meet certain conditions. Additionally, we provide a numerical example to illustrate our theoretical results.

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Section: Introductionmentioning

confidence: 99%

Point process of clusters for a stationary Gaussian random field on a lattice

Yingyin Lu,

Jinhui Guo

2023

PMS

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Second-order Asymptotics on Distributions of Maxima of Bivariate Elliptical Arrays

Liao

Weng

Peng

2018

Acta. Math. Sin.-English Ser.

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Let {(ξ ni , η ni ), 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as (S 1 , ρ n S 1 + 1 − ρ 2 n S 2 ), ρ n ∈ (0, 1), where (S 1 , S 2 ) is a bivariate spherical random vector. For the distribution function of radius S 2 1 + S 2 2 belonging to the max-domain of attraction of the Weibull distribution, Hashorva (2006) derived the limiting distribution of maximum of this triangular array if convergence rate of ρ n to 1 is given. In this paper, under the refinement of the rate of convergence of ρ n to 1 and the second-order regular variation of the distributional tail of radius, precise second-order distributional expansions of the normalized maxima of bivariate elliptical triangular arrays are established.

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Joint behavior of point processes of clusters and partial sums for stationary bivariate Gaussian triangular arrays

Guo

2022

Ann Inst Stat Math

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Maxima of a triangular array of multivariate Gaussian sequence

Cited by 5 publications

References 12 publications

Point process of clusters for a stationary Gaussian random field on a lattice

Point process of clusters for a stationary Gaussian random field on a lattice

Second-order Asymptotics on Distributions of Maxima of Bivariate Elliptical Arrays

Joint behavior of point processes of clusters and partial sums for stationary bivariate Gaussian triangular arrays

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