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April 2016 Optimal shrinkage estimation of mean parameters in family of distributions with quadratic variance
Xianchao Xie, S. C. Kou, Lawrence Brown
Ann. Statist. 44(2): 564-597 (April 2016). DOI: 10.1214/15-AOS1377

Abstract

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.

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Xianchao Xie. S. C. Kou. Lawrence Brown. "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

Information

Received: 1 February 2015; Revised: 1 August 2015; Published: April 2016
First available in Project Euclid: 17 March 2016

zbMATH: 1347.60017
MathSciNet: MR3476610
Digital Object Identifier: 10.1214/15-AOS1377

Subjects:
Primary: 60K35

Keywords: asymptotic optimality , hierarchical model , location-scale family , NEF-QVF , quadratic variance function , shrinkage estimator , unbiased estimate of risk

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 2 • April 2016
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