Moments and Quadratic Forms of Matrix Variate Skew Normal Distributions
In 2007, Domínguez-Molina et al. obtained the moment generating function (mgf) of the matrix variate closed skew normal distribution. In this paper, we use their mgf to obtain the first two moments and some additional properties of quadratic forms for the matrix variate skew normal distributions. The quadratic forms are particularly interesting because they are essentially correlation tests that introduce a new type of orthogonality condition.
Zheng, Shimin; Knisley, Jeff; and Wang, Kesheng. 2016. Moments and Quadratic Forms of Matrix Variate Skew Normal Distributions. Communications in Statistics - Theory and Methods. Vol.45(3). 794-803. https://doi.org/10.1080/03610926.2013.851230 ISSN: 0361-0926