Optimal shrinkage estimation of mean parameters in family of distributions with quadratic variance
针对具有二次方差函数的分布族，提出一类半参数/参数收缩估计量并证明其渐近最优性，通过模拟和实际数据验证了方法的有效性。
This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semi-parametric/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.