Wishart–Laplace distributions associated with matrix quadratic forms

Applications of quadratic D-forms to generalized quadratic forms

In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.

On the Distribution of Matrix Quadratic Forms

Martin Ohlson and Timo Koski, On the Distribution of Matrix Quadratic Forms, 2012, Communications in Statistics Theory and Methods, (41), 18, 3403-315. Communications in Statistics Theory and Methods is available online at informaworld TM : http://dx.doi.org/10.1080/03610926.2011.563009 Copyright: Taylor & Francis: STM, Behavioural Science and Public Health Titles / Taylor & Francis http://www....

On a quadratic matrix equation associated with an M-matrix∗

We study the quadratic matrix equation X2 − EX − F = 0, where E is diagonal and F is an M -matrix. Quadratic matrix equations of this type arise in noisy Wiener–Hopf problems for Markov chains. The solution of practical interest is a particular M -matrix solution. The existence and uniqueness of M -matrix solutions and numerical methods for finding the desired M -matrix solution are discussed b...

Two simple approximations to the distributions of quadratic forms.

Many test statistics are asymptotically equivalent to quadratic forms of normal variables, which are further equivalent to T = sigma(d)(i=1) lambda(i)z(i)(2) with z(i) being independent and following N(0,1). Two approximations to the distribution of T have been implemented in popular software and are widely used in evaluating various models. It is important to know how accurate these approximat...

I the Distributions of Quadratic Forms on Normal Random Variables