Bayesian Shrinkage Estimation for Stratified Count Data

TL;DR

This paper develops Bayesian shrinkage estimators for stratified Poisson count data, leveraging side information and conjugate priors to improve estimation accuracy and establish theoretical optimality conditions.

Contribution

It introduces a new Bayesian shrinkage approach for Poisson parameters using conjugate priors and analyzes their risk properties, including minimaxity and admissibility.

Findings

Bayesian estimators outperform direct estimators under certain conditions

Conditions for estimator domination are derived

Minimaxity and admissibility are established for specific priors

Abstract

In this paper, we consider simultaneous estimation of Poisson parameters in situations where we can use side information in aggregated data. We use standardized squared error and entropy loss functions. Bayesian shrinkage estimators are derived based on conjugate priors. We compare the risk functions of direct estimators and Bayesian estimators with respect to different priors that are constructed based on different subsets of observations. We obtain conditions for domination and also prove minimaxity and admissibility in a simple setting.