Abstract
Motivated by a heteroscedastic random effects setting of meta-analysis, a general model for the between-study variance is studied from the decision-theoretic point of view. This model leads to estimation of a linear in the variance reciprocals, random function or to simultaneous inference on curve-confined natural parameters of independent heterogeneous \(\chi ^2\)-random variables with given degrees of freedom. A form of the Stein phenomenon for the suggested loss functions is noted; the exact minimax value is determined, and minimax estimators are derived.
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Rukhin, A.L. Decision-theoretic issues in heterogeneity variance estimation. Ann Inst Stat Math 68, 571–588 (2016). https://doi.org/10.1007/s10463-015-0505-1
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DOI: https://doi.org/10.1007/s10463-015-0505-1