平衡随机模型中方差分量的非负估计

众所周知, 对于平衡随机模型, 方差分量的方差分析估计为一致最小方差无偏估计. 本文基于方差分量的方差分析估计, 构造了一个二次不变估计类, 它包含了一些常用重要估计. 证明了该估计类在一定条件下在均方误差意义下一致优于方差分析估计, 并在此估计类基础上, 给出了方差分量的两种非负估计, 它们在均方误差意义下分别一致优于方差分析估计和限制极大似然估计, 且有显式解、容易计算.

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. theestimators from this class have explicit expressions and are easily computable.