Distribution theory of quadratic forms for matrix multivariate elliptical distribution |
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Authors: | José A. Dí az-Garcí a |
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Affiliation: | Universidad Autónoma Agraria Antonio Narro, Department of Statistics and Computation, 25315 Buenavista, Saltillo, Coahuila, Mexico |
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Abstract: | 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. |
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Keywords: | Quadratic forms Spherical functions Jacobians Elliptical models Real, complex, quaternion and octonion random matrices |
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