Restricted likelihood representation and decision-theoretic aspects of meta-analysis

Abstract

In the random-effects model of meta-analysis a canonical representation of the restricted likelihood function is obtained. This representation relates the mean effect and the heterogeneity variance estimation problems. An explicit form of the variance of weighted means statistics determined by means of a quadratic form is found. The behavior of the mean squared error for large heterogeneity variance is elucidated. It is noted that the sample mean is not admissible nor minimax under a natural risk function for the number of studies exceeding three.