Moments and quadratic forms of matrix variate skew normal distributions

ABSTRACT

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.

Keywords:

• Correlation
• Matrix variate
• Matrix variate closed skew normal distributions
• Moment
• Moment generating function
• Skew normal distribution
• Quadratic form

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62H10
• Secondary 62H05

Acknowledgments

The authors would like to thank the reviewers for their close reading of the manuscript and their many excellent suggestions for improving this effort. The authors are also thankful to Yan Cao and Yang Chen for typing this paper using Latex.