Decision-Theoretic Issues in Heterogeneity Variance Estimation
Andrew L. Rukhin
In a random-effects setting of meta-analysis the between-study variance estimation is studied from the decision-theoretic point of view. The problem concerns simultaneous inference on curve-confined natural parameters of independent heterogeneous chi-squared random variables with given degrees of freedom. A form of the Stein phenomenon for the suggested loss function is noted, and the exact minimax value is determined. Second order minimax estimators are also derived.