Shrinkage estimation of rate statistics

TL;DR

This paper introduces a Bayesian shrinkage estimator for crime rates that improves accuracy and coverage over traditional methods by shrinking local rates toward the national average, especially considering town size.

Contribution

It proposes a new Bayesian shrinkage estimator for rate statistics that outperforms maximum likelihood estimates in risk and coverage, with applications to crime rates.

Findings

Outperforms maximum likelihood in global risk

Provides better coverage properties

Effective for small sample sizes

Abstract

This paper presents a simple shrinkage estimator of rates based on Bayesian methods. Our focus is on crime rates as a motivating example. The estimator shrinks each town's observed crime rate toward the country-wide average crime rate according to town size. By realistic simulations we confirm that the proposed estimator outperforms the maximum likelihood estimator in terms of global risk. We also show that it has better coverage properties.