A Matrix Variate Closed Skew-Normal Distribution with Applications to Stochastic Frontier Analysis

Abstract

In this article, we introduce the matrix extension of the closed skew-normal distribution and give two constructions for it: a marginal one and another based on hidden truncation. Important basic properties of the distribution are presented such as its closure under linear transformation and moment generating function. We also give distributional results for quadratic forms involving random matrices distributed according to two particular cases of it. Using an additive construction, we derive a submodel which can be employed to describe the compound error structure of a very general multivariate stochastic frontier model. Finally, we consider the skew-elliptical extension of the proposed distribution.

Keywords:

• Chi-square distribution
• Compound error
• Hidden truncation
• Linear transformation
• Quadratic forms
• Skew-elliptical distribution
• Wishart distribution

Mathematics Subject Classification:

• Primary 62E15
• Secondary 62H10

Acknowledgments

This work was partially supported by the research projects 45974-F CONACYT-México and SEJ2004-04101-ECON (Spanish Ministry of Education) and by CONCYTEG grant 04-16-K117-028.