Distribution theory of quadratic forms with matrix argument
J. Diaz-Garcia. (2012)cite arxiv:1210.5283Comment: 17 pages. arXiv admin note: text overlap with arXiv:1207.1993, arXiv:1010.1799, arXiv:1012.5856, arXiv:1011.5083.
Abstract
This paper proposes the density and characteristic functions of a general
matrix quadratic form $X^*AX$, when $A =
A^*$, $X$ 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.
Description
Distribution theory of quadratic forms with matrix argument
%0 Generic
%1 diazgarcia2012distribution
%A Diaz-Garcia, Jose A.
%D 2012
%K distributions multivariate quadratic-forms statistics
%T Distribution theory of quadratic forms with matrix argument
%U http://arxiv.org/abs/1210.5283
%X This paper proposes the density and characteristic functions of a general
matrix quadratic form $X^*AX$, when $A =
A^*$, $X$ 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.
@misc{diazgarcia2012distribution,
abstract = {This paper proposes the density and characteristic functions of a general
matrix quadratic form $\mathbf{X}^{*}\mathbf{AX}$, when $\mathbf{A} =
\mathbf{A}^{*}$, $\mathbf{X}$ has a matrix multivariate elliptical distribution
and $\mathbf{X}^{*}$ denotes the usual conjugate transpose of $\mathbf{X}$.
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.},
added-at = {2015-12-23T19:52:54.000+0100},
author = {Diaz-Garcia, Jose A.},
biburl = {https://www.bibsonomy.org/bibtex/2261f33264742583be67e3855614fe23a/shabbychef},
description = {Distribution theory of quadratic forms with matrix argument},
interhash = {8a3afb4f3d8edad4f2af5db727aa5166},
intrahash = {261f33264742583be67e3855614fe23a},
keywords = {distributions multivariate quadratic-forms statistics},
note = {cite arxiv:1210.5283Comment: 17 pages. arXiv admin note: text overlap with arXiv:1207.1993, arXiv:1010.1799, arXiv:1012.5856, arXiv:1011.5083},
timestamp = {2015-12-23T19:52:54.000+0100},
title = {Distribution theory of quadratic forms with matrix argument},
url = {http://arxiv.org/abs/1210.5283},
year = 2012
}