On Spectral Decomposition Estimates in Mixed Linear Models

This paper gives a survey of the recent developments on parameter estimation in linear mixed model. The covariance matrix in balanced analysis of variance mixed linear models has a specific structure. For this model, 1 proposed a new approach, spectral decomposition method, to estimate parameters. The merits of the approach is to provide independent estimates of fixed effects and variance components simultaneously, the former is linear and late quadratic. 2--9 established some further properties of the new estimates and corresponding estimates of covariance matrix with risk function. These papers also obtained some relations among the analysis of variance estimate, maximum likelihood estimate, restricted maximum likelihood estimate, minimum norm quadratic unbiased estimate and new estimates. Finally, some open problems are proposed.