The second-order derivatives of matrices of eigenvalues and eigenvectors with an application to generalized \(F\)-statistic
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.
scientific article; zbMATH DE number 2105739