Harmonic mean approach to unbalanced mixed effects models under heteroscedastic variances

In this paper we consider unbalanced mixed models (Scheffe's model) under heteroscedastic variances. By using the harmonic mean approach, It is shown that the problems appear to be anologous to those problems from balanced mixed models under homoscedastic variance. Thus, by using harmonic mean approach, statistical inferences about fixed effects and variance components are derived by using those from balanced models under homoscedastic variance. Laguerre polynomial expansion is used Lo approximate sampling distributions of relevant statistics.