Optimal shrinkage estimation of mean parameters in family of distributions with quadratic variance

TL;DR

This paper develops and analyzes optimal shrinkage estimators for mean parameters in distributions with quadratic variance, demonstrating their theoretical properties and practical effectiveness through simulations and real data applications.

Contribution

Introduces a class of semiparametric and parametric shrinkage estimators with proven asymptotic optimality for distributions with quadratic variance functions.

Findings

Proposed estimators outperform existing methods in simulations.

Estimation methods show strong performance on real data.

Theoretical results confirm asymptotic optimality.

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.