Construction, properties and statistical applications of positive definite intraclass matrix

Abstract

Given a positive definite (p.d.) matrix with real entries, it is possible to construct a p.d. intraclass matrix whose diagonal and off-diagonal elements are chosen as the averages of the diagonal elements and off-diagonal elements of the former matrix. Exploiting the very special structure of the latter matrix various interesting propositions are established. Statistical applications of such matrices are surveyed.

Keywords:

• positive definite matrix
• intraclass matrix
• trace
• norm
• eigenvalue
• ill-conditioned matrix

AMS Subject Classifications:

• 15A18
• 15A60
• 62H25

Acknowledgements

The author is grateful to Prof Ravindra B. Bapat and Prof Steve Kirkland for their unstinting suggestions which led to substantive improvement in this article.