This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semiparametric/parametric shrinkage estimators and establish their asymptotic optimality properties. Two specific cases, the location-scale family and the natural exponential family with quadratic variance function, are then studied in detail. We conduct a comprehensive simulation study to compare the performance of the proposed methods with existing shrinkage estimators. We also apply the method to real data and obtain encouraging results.
"Optimal shrinkage estimation of mean parameters in family of distributions with quadratic variance." Ann. Statist. 44 (2) 564 - 597, April 2016. https://doi.org/10.1214/15-AOS1377