OPTIMAL SHRINKAGE ESTIMATION OF MEAN PARAMETERS IN FAMILY OF DISTRIBUTIONS WITH QUADRATIC VARIANCE

被引：18

作者：

Xie, Xianchao ^{[1
]}

Kou, S. C. ^{[2
]}

Brown, Lawrence ^{[3
]}

机构：

[1] Two Sigma Investments LLC, 100 Ave Amer,Floor 16, New York, NY 10013 USA

[2] Harvard Univ, Dept Stat, Cambridge, MA 02138 USA

[3] Univ Penn, Wharton Sch, Philadelphia, PA 19104 USA

来源：

ANNALS OF STATISTICS | 2016年 / 44卷 / 02期

基金：

美国国家科学基金会;

关键词：

Hierarchical model; shrinkage estimator; unbiased estimate of risk; asymptotic optimality; quadratic variance function; NEF-QVF; location-scale family; EMPIRICAL BAYES ESTIMATION; POISSON; ADMISSIBILITY; PREDICTION; VECTOR;

D O I：

10.1214/15-AOS1377

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：564 / 597

页数：34

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