In the random-effects model of meta-analysis a canonical representation of the restricted likelihood function is obtained. The relationship between the common mean estimators and the heterogeneity variance estimators is explored via this representation. An explicit form of weighted means statistics variance is found.The behavior of the quadratic risk for large heterogeneity variance is elucidated. It is noted that the sample mean is not admissible or minimax when the number of studies is larger than three.
Journal of the Royal Statistical Society Series B-Statistical Methodology
Decision-Theoretic Aspects of Meta-Analysis, Journal of the Royal Statistical Society Series B-Statistical Methodology, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=912771
(Accessed December 5, 2023)