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平衡三阶段嵌套随机效应模型中方差分量估计量的均方误差比较AI 解读

Various estimators of variance components for the balanced three-stage nested random effects model are compared under standard assumptions of normality and independence of random effects, using MSE as the measure of performance. Several results are proven, demonstrating the inequality relationships on MSE of the unbiased, restricted maximum likelihood and maximum likelihood, and several modifications of the unbiased and maximum likelihood estimators as introduced here,…

高阶层级随机效应模型中的贝叶斯等变估计量AI 解读

Summary The Bayes equivariant estimators of the variance components (Zacks, 1970, 1971) are characterized in the case of r-stage hierarchical random effects models when the random effects are normally distributed and are mutually and completely independent. Non-trivial Bayes equivariant estimators are derived using a special prior distribution for the three-stage hierarchical model. It is observed that for the squared error loss function every Bayes equivariant estimator of…