Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 3, 370--394

TOTALLY ORDERED MULTIVARIATE LINEAR MODELS

By

STEEN A. ANDERSON, Indiana University, Bloomington, U. S. A.

JOHN I. MARDEN, University of Illinois, Urbana, U.S. A.

And

MICHAEL D. PERLMAN, University of Washington, Seattle, U.S.A.

 

SUMMARY. many multivariate normal linear models and testing problems with unrestricted covariance structure that are amenable to explicit (non-iterative) likelihood analysis have the common property of invariance under a full mblock-triangular matrix group. In this paper we study the general theory ordered multivariate linear model, defined by this algebraic condition of invariance under a full block-triangular group. It is shown that this algebraic characterization allows an explicit likelihood analysis of all such models, thereby unifying the treatment of the many examples that have appeared in the literature and extending the scope of this treatment to the widest possible class.

Subject classification. 62H10,62H12,62H15

FULL PAPER.

This article in Mathematical Reviews.