Spectral analysis of the fourth moment matrix
type: Item
instance of: scholarly article
title: Spectral analysis of the fourth moment matrix
zbMATH Open document ID: 1222.15015
published in: Linear Algebra and its Applications
publication date: 2011-07-15T00:00:00Z
review text: Let \(x = (X_1, \dots , X_d)\) be a \(d\)-dimensional random vector satisfying \(E(X_i^4)<+\infty\), for \(i = 1,\dots, d\). The fourth moment of \(x\) is the \(d^2\times d^2\) symmetric and positive semidefinite matrix \(\mu_4(x)=E(x\otimes x^T\otimes x\otimes x^T)\), where \(\otimes\) denotes the Kronecker product. In this paper, a lower bound for the fourth moment of \(x\) dominant eigenvalue is provided. It is shown that its eigenvectors corresponding to positive eigenvalues are vectorized symmetric matrices. Fourth moments of standardized and exchangeable random vectors are examined.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 60G09
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 5924555
zbMATH Keywords: commutation matrix
zbMATH Keywords: exchangeability
zbMATH Keywords: fourth moment
zbMATH Keywords: skew-symmetric matrix
zbMATH Keywords: symmetric matrix
zbMATH Keywords: positive semidefinite matrix
zbMATH Keywords: eigenvalue
zbMATH Keywords: eigenvectors
author: Nicola M. R. Loperfido
reviewed by: C. M.da Fonseca
MaRDI profile type: Publication
full work available at URL: j.laa.2011.03.053
OpenAlex ID: W2002276754
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DOI: 10.1016/J.LAA.2011.03.053
description: scientific article; zbMATH DE number 5924555