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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
Department of Mathematics, Stockholm University, Stockholm, Sweden.
Örebro University, Örebro University School of Business. Department of Statistics.ORCID iD: 0000-0002-1395-9427
Institute of Statistics, Leibniz University of Hannover, Hannover, Germany.
2019 (English)In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 46, no 2, p. 636-660Article in journal (Refereed) 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 to infinity such that p/n → c ∈ [0, +∞) when the sample covariance matrix does not need to be invertible and p/n → c ∈ [0, 1) otherwise.

##### Place, publisher, year, edition, pages
John Wiley & Sons, 2019. Vol. 46, no 2, p. 636-660
##### Keywords [en]
Normal mixtures, skew normal distribution, large dimensional asymptotics, stochas- tic representation, random matrix theory
##### National Category
Probability Theory and Statistics
##### Identifiers
ISI: 000465606900012Scopus ID: 2-s2.0-85061927074OAI: oai:DiVA.org:oru-61246DiVA, id: diva2:1146950
##### Funder
Swedish Research Council, 2013-5180Riksbankens Jubileumsfond, P13-1024: 1Available from: 2017-10-04 Created: 2017-10-04 Last updated: 2019-06-19Bibliographically approved

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##### In the same journal
Scandinavian Journal of Statistics
##### On the subject
Probability Theory and Statistics

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Cite
Citation style
• apa
• harvard1
• ieee
• modern-language-association-8th-edition
• vancouver
• Other style
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• fi-FI
• nn-NO
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