We study properties of the maximum h‐likelihood estimators for random effects in clustered data. To define optimality in random effects predictions, several foundational concepts of statistics such as likelihood, unbiasedness, consistency, confidence distribution and the Cramer–Rao lower bound are extended. Exact probability statements about interval estimators for random effects can be made asymptotically without a prior assumption. Using the binary‐matched pair example, we illustrated that the use of random effects recover information, leading to the boon on estimating treatment effects.

中文翻译：

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聚类数据中的h似然估计的属性

我们研究了群集数据中随机效应的最大h可能性估计量的性质。为了定义随机效应预测的最优性，扩展了统计学的几个基本概念，例如似然性，无偏性，一致性，置信度分布和Cramer-Rao下界。无需先验假设就可以渐近地得出有关随机效应的区间估计量的精确概率陈述。以二进制匹配对为例，我们说明了使用随机效应可恢复信息，从而使估计治疗效应受益匪浅。