Harmonic mean approach to uunbalanced random effects models under heteroscedasticity

In this paper we consider unbalanced random effects models under heteroscedastic variances. By using' the harmonic mean approach, it is shown that the problems are analogous to those from balanced random effects models under horaoscedastic variances. Thus, by using the harmonic mean approach, statistical inferences about variance components are derived by using procedures from balanced models under homoscedastic variances. Laguerre polynomial expansion is used to approximate the sampling distributions of relevant statistics.