The Spectral Decomposition Of Covariance Matrix And Its Application In Multi Variate Linear Mixed Models

This paper mainly studies the spectral decomposition of the covariance matrix and esti-mates of variance components matrix in the balance multivariate linear mixed models.First, the two methods of spectral decomposition of a linear mixed model covariance matrix are extended to balance multivariate linear mixed models, then get two methods of spectral decomposition of covariance matrix in the balance multivariate linear mixed models.Second, based on the spectral decomposition of balance multivariate linear mixed model, we study a new estimate of variance components matrix in balance multivariate linear mixed models called spectral decomposition estimate, and introduce the properties of the spectral decomposition estimate,at the same time the spectral decomposition estimated applied to several common multivariate linear mixed models.