An empirical study of the estimation of eigenvalues in connection with non-negative estimation of variance components of a one-way random effect model

Abstract

A variance component is, by definition, positive. Nevertheless, the MLE and ANOVA estimate of treatment variance of σ 2 τ, of a one-way random effect model can be negative. Recently, a multivariate approach has been suggested by Sutradhar (1988) which always produces non-negative estimate of σ 2 τ. The multivariate approach exploits the estimates of the eigenvalues of the covariance matrix of the model in estimating variance components. The success of the estimation procedure depends on the precise estimation of the eigenvalues. This paper through a simulation study examines the behaviour of the estimates of eigenvalues of the covariance matrix of the model for various sample sizes. Several approaches for the estimation of eigenvalues have been considered and compared.