Stochastic monotonicity of a distribution family associated with matrix projections and its application

Abstract

This article defines a distribution family based on the distribution of a random variable associated with the projections of a normally distributed random matrix with unknown mean onto a linear space and onto a closed convex cone. The stochastic monotonicity property of the distributions in the family is established. This property finds the application in the proving the unbiasedness of a likelihood ratio test in a multivariate order restricted model.

Keywords:

• Closed convex cone
• matrix projection
• matrix with normal distributions
• multivariate order restriction
• unbiased test

AMS (2010) SUBJECT CLASSIFICATION:

• Primary 62F30
• Secondary 62H10