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Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix-variate location mixture of normal distributions
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.ORCID-id: 0000-0001-7855-8221
Rekke forfattare: 32019 (engelsk)Inngår i: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 46, nr 2, s. 636-660Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

In this paper, we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal distributions. The central limit theorem is derived for the product of the sample covariance matrix and the sample mean vector. Moreover, we consider the product of the inverse sample covariance matrix and the mean vector for which the central limit theorem is established as well. All results are obtained under the large-dimensional asymptotic regime, where the dimension p and the sample size n approach infinity such that p/n -> c is an element of [0, + infinity) when the sample covariance matrix does not need to be invertible and p/n -> c is an element of [0,1) otherwise.

sted, utgiver, år, opplag, sider
2019. Vol. 46, nr 2, s. 636-660
Emneord [en]
large-dimensional asymptotics, normal mixtures, random matrix theory, skew normal distribution, stochastic representation
Identifikatorer
ISI: 000465606900012OAI: oai:DiVA.org:su-169237DiVA, id: diva2:1326316
Tilgjengelig fra: 2019-06-18 Laget: 2019-06-18 Sist oppdatert: 2019-06-18bibliografisk kontrollert

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Bodnar, TarasParolya, Nestor
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Scandinavian Journal of Statistics

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