The second-order derivatives of matrices of eigenvalues and eigenvectors with an application to generalized \(F\)-statistic (Q1881065)
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scientific article; zbMATH DE number 2105739
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The second-order derivatives of matrices of eigenvalues and eigenvectors with an application to generalized \(F\)-statistic |
scientific article; zbMATH DE number 2105739 |
Statements
The second-order derivatives of matrices of eigenvalues and eigenvectors with an application to generalized \(F\)-statistic (English)
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4 October 2004
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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.
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matrix derivative
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hypothesis testing
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normal population
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bias estimate
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