On shift permutation invariance, covariance structures, and Toeplitz matrices

Authors

  • Tatjana Nahtman University of Tartu
  • Dietrich von Rosen Swedish University of Agricultural Sciences

DOI:

https://doi.org/10.12697/ACUTM.2006.10.08

Keywords:

covariance structures, eigenspace, shift invariance, marginal permutations, reparametrization, spectrum, Toeplitz matrix

Abstract

The objective of this paper is to present a comprehensive study of shift permutation invariant covariance structures in linear models. It follows that the corresponding covariance matrices belong to the class of symmetric circular Toeplitz matrices. Results for the spectrum of shift permutation invariant covariance matrices of random factors in linear models are given. Among others the results are of use when reparametrization conditions are imposed in order to perform inference based on a unique set of parameters.

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Author Biographies

Tatjana Nahtman, University of Tartu

Institute of Mathematical Statistics

Dietrich von Rosen, Swedish University of Agricultural Sciences

Department of Biometry and Engineering

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Published

2006-12-31

Issue

Section

Articles