Properties of h-Likelihood Estimators in Clustered Data

Abstract

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.