Mean Shrinkage Estimation for Diagonal Multivariate Natural Exponential Families

• Activity Number: 347 - Nonparametric Hybrid Methods
• Type: Contributed
• Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Nikolas Siapoutis* and Bharath Kumar Sriperumbudur and Donald Richards
• Companies: The Pennsylvania State University and The Pennsylvania State University and The Pennsylvania State University
• Keywords: diagonal multivariate natural exponential families; shrinkage estimator; unbiased estimate of risk; asymptotic optimality

Abstract

Shrinkage estimators have been studied widely in statistics and have profound impact in many applications. In this paper, we discuss the simultaneous estimation of the mean parameters of diagonal multivariate natural exponential families. In studying the family of distributions with quadratic diagonal covariance matrices, we propose two classes of semi-parametric shrinkage estimators for the mean parameters and construct unbiased estimators of the risk from estimating those parameters. Further, we establish the asymptotic optimality of the shrinkage estimators under squared error loss as n, the sample size, tends to infinity. Finally, we consider the case of the diagonal multivariate natural exponential families, which include the multivariate normal, Poisson, gamma, multinomial and negative multinomial distributions, and we establish the asymptotic optimality under weaker assumptions.