Nonnegative Estimation of Variance Components in General Random Effect Model with Balanced Data

For general random effect model with balanced data, it is well-known that analysis of variance estimate (ANOVAE) of variance components is the uniformly minimum variance unbiased estimate (UMVUE). This paper establishes a class of invariant quadratic estimators based on ANOVAE of variance components, which contains several important estimators. In the sense of mean square error, it is proved that this class is uniformly superior to ANOVAE under certain conditions. On the basis of this class, we obtain two nonnegative estimators of variance components, which are uniformly superior to ANOVAE and restricted maximum likelihood estimate (REMLE) in the sense of mean square error,respectively. the estimators from this class have explicit expressions and are easily computable.