Optimal shrinkage estimation of mean parameters in family of distributions with quadratic variance. (English) Zbl 1347.60017
Summary: 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.
MSC:
| 60F05 | Central limit and other weak theorems |
| 62F12 | Asymptotic properties of parametric estimators |
| 65C60 | Computational problems in statistics (MSC2010) |
Keywords:
shrinkage estimator; hierarchical model; unbiased risk estimate; asymptotic optimality; quadratic variance function; location-scale familySoftware:
mixfdrReferences:
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