Distribution theory of quadratic forms for matrix multivariate elliptical distribution

作者：Diaz Garcia Jose A^*

来源：Journal of Statistical Planning and Inference, 2013, 143(8): 1330-1342.

DOI：10.1016/j.jspi.2013.03.024

• Quadratic forms
• Spherical functions
• Jacobians
• Elliptical models
• Real, complex, quaternion and octonion random matrices

This paper proposes the density and characteristic functions of a general matrix quadratic form X*AX, when A = A* is a positive semidefinite matrix, X has a matrix multivariate elliptical distribution and X* denotes the usual conjugate transpose of X. These results are obtained for real normed division algebras. With particular cases we obtained the density and characteristic functions of matrix quadratic forms for matrix multivariate normal, Pearson type VII, t and Cauchy distributions.

• 出版日期2013-8