Gaussian approximation of perturbed chi-square risks

Dȩbicki, Krzysztof; Hashorva, Enkelejd; Ji, Lanpeng

doi:10.4310/sii.2014.v7.n3.a6

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Cited by 6 publications

References 31 publications

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Maxima and minima of independent and non-identically distributed bivariate Gaussian triangular arrays

Peng

2016

Extremes

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Abstract. In this paper, joint limit distributions of maxima and minima on independent and non-identically distributed bivariate Gaussian triangular arrays is derived as the correlation coefficient of ith vector of given nth row is the function of i/n. Furthermore, second-order expansions of joint distributions of maxima and minima are established if the correlation function satisfies some regular conditions.

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Maxima and minima of independent and non-identically distributed bivariate Gaussian triangular arrays

Peng

2016

Extremes

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Higher-order expansions of distributions of maxima in a Hüsler-Reiss model

Hashorva

Peng

Weng

2014

Methodol Comput Appl Probab

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The max-stable Hüsler-Reiss distribution which arises as the limit distribution of maxima of bivariate Gaussian triangular arrays has been shown to be useful in various extreme value models. For such triangular arrays, this paper establishes higher-order asymptotic expansions of the joint distribution of maxima under refined Hüsler-Reiss conditions. In particular, the rate of convergence of normalized maxima to the Hüsler-Reiss distribution is explicitly calculated.

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Extremes and limit theorems for difference of chi-type processes

Albin

Hashorva

et al. 2016

ESAIM: PS

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Abstract. Let {ζ (κ) m,k (t), t ≥ 0}, κ > 0 be random processes defined as the differences of two independent stationary chi-type processes with m and k degrees of freedom. In this paper we derive the asymptotics of P sup t∈[0,T ] ζ (κ) m,k (t) > u , u → ∞ under some assumptions on the covariance structures of the underlying Gaussian processes. Further, we establish a Berman sojourn limit theorem and a Gumbel limit result.

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Gaussian approximation of perturbed chi-square risks

Abstract: In this paper we show that the conditional distribution of perturbed chi-quare risks can be approximated by certain distributions including the Gaussian ones. Our results are of interest for conditional extreme value models and multivariate extremes as shown in three applications.

Cited by 6 publications

References 31 publications

Maxima and minima of independent and non-identically distributed bivariate Gaussian triangular arrays

Maxima and minima of independent and non-identically distributed bivariate Gaussian triangular arrays

Higher-order expansions of distributions of maxima in a Hüsler-Reiss model

Extremes and limit theorems for difference of chi-type processes

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