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On n/p-Asymptotic Distribution of Vector of Weighted Traces of Powers of Wishart Matrices
Linnaeus University, Växjö, Sweden.ORCID iD: 0000-0002-0341-7472
Swedish University of Agricultural Sciences, Uppsala, Sweden.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-9896-4438
2018 (English)In: The Electronic Journal of Linear Algebra, ISSN 1537-9582, E-ISSN 1081-3810, Vol. 33, p. 24-40Article in journal (Refereed) Published
Abstract [en]

The joint distribution of standardized traces of $\frac{1}{n}XX'$ and of $\Big(\frac{1}{n}XX'\Big)^2$, where the matrix $X:p\times n$ follows a matrix normal distribution is proved asymptotically to be multivariate normal under condition $\frac{{n}}{p}\overset{n,p\rightarrow\infty}{\rightarrow}c>0$. Proof relies on calculations of asymptotic moments and cumulants obtained using a recursive formula derived in Pielaszkiewicz et al. (2015). The covariance matrix of the underlying vector is explicitely given as a function of $n$ and $p$.

Place, publisher, year, edition, pages
Pensacola, FL, United States: International Linear Algebra Society , 2018. Vol. 33, p. 24-40
Keywords [en]
Wishart matrix, multivariate normal distribution, spectral distribution, spectral moments, covariance matrix
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-152113DOI: 10.13001/1081-3810.3732OAI: oai:DiVA.org:liu-152113DiVA, id: diva2:1256652
Available from: 2018-10-17 Created: 2018-10-17 Last updated: 2019-08-05Bibliographically approved

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Pielaszkiewicz, Jolantavon Rosen, DietrichSingull, Martin

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