Bayes estimators of heterogeneity variance and T-systems

The considered problem concerns simultaneous inference for curve-confined natural parameters of independent, heterogeneous gamma random variables with known shape parameters. A loss function is suggested that is motivated by meta-analysis, and some properties of the minimax value of the corresponding risk are obtained. Bayes estimators and quadrature formulas for their numerical evaluation are provided, along with Monte Carlo simulations and comparisons of numerical implementations of several alternative estimators.