%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 }