  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.
