The second-order derivatives of matrices of eigenvalues and eigenvectors with an application to generalized F-statistic

✍ Scribed by Olga Dunajeva

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 207 KB
• Volume: 388
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2003.08.019

✦ Synopsis

In this paper we derive the second-order derivatives of an orthogonal matrix of eigenvectors and of a matrix of eigenvalues of a real symmetric matrix. Obtained expressions depend on the first-order derivatives of these matrices, which were presented in Linear Algebra Appl. 264 (1997) 489. These results we use to find the main term of the bias of a generalized F -statistic [Biometrical J. 38 (1996) 5] in the case of normal population. A simulation experiment is carried out, in which we compare the sample mean and unbiased estimator of F -statistic with its asymptotic mean, which was obtained in Linear Algebra Appl. 321 (2000) 27.