Some Properties of Spectral Decomposition Estimate of Variance Components

Although there exist many estimates of variance components in linear mixed effects models, only the spectral decomposition estimate （SDE） and analysis of variance estimate （ANOVAE） have closed form in the general case. In this paper we compare the SDE with the ANOVAE in the linear mixed model with two variance components. Our results show that these two estimates of the variance components have the equal variance under some conditions. Thus the SDE shares some optimalities of the ANOVAE. Two examples are given to illustrate our theoretical results.