Shift permutation invariance in linear random factor models

Abstract

The objective of this paper is to consider shift invariance of random factors in linear models. Marginally shift invariant interaction factors are treated. The random factors are described via their covariance matrices and it is shown that shift invariance implies Toeplitz covariance matrices and marginally shift invariance implies block Toeplitz covariance matrices. In order to get interpretable linear models reparameterization is taken place and it is shown that by putting restrictions on the spectrum of the Toeplitz matrices natural reparameterization conditions are obtained

Keywords

Block Toeplitz matrix; covariance structures; eigenspace; invariance; K-way tables; marginal permutations; reparameterization; shift invariance; spectrum; Toeplitz matrix

Published in

Research report (Centre of Biostochastics)
2005, number: 2005:6
Publisher: Centre of Biostochastics, Swedish University of Agricultural Sciences

SLU Authors

• von Rosen, Dietrich

  • Department of Energy and Technology, Swedish University of Agricultural Sciences
    

UKÄ Subject classification

Agricultural Science
Probability Theory and Statistics

Permanent link to this page (URI)

https://res.slu.se/id/publ/6849