The second-order derivatives of matrices of eigenvalues and eigenvectors with an application to generalized \(F\)-statistic
type: Item
instance of: scholarly article
title: The second-order derivatives of matrices of eigenvalues and eigenvectors with an application to generalized \(F\)-statistic
zbMATH Open document ID: 1065.15010
author: Olga Dunajeva
published in: Linear Algebra and its Applications
publication date: 2004-10-04T00:00:00Z
review text: The author develops formulas for the second derivative of the matrix of eigenvalues and orthogonal eigenvectors of a real symmetric matrix. The result is used to find a better estimate for the bias of the generalized \(F\)-statistic as that given by \textit{J. Läuter} [Biometrics 52, No. 3, 964--970 (1996; Zbl 0867.62049)] in case of a normal population via Taylor expansion. A simulation experiment is included.
reviewed by: Frank Uhlig
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 2105739
zbMATH Keywords: matrix derivative
zbMATH Keywords: hypothesis testing
zbMATH Keywords: normal population
zbMATH Keywords: bias estimate
MaRDI profile type: Publication
full work available at URL: j.laa.2003.08.019
OpenAlex ID: W1965892347
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DOI: 10.1016/J.LAA.2003.08.019
description: scientific article; zbMATH DE number 2105739