Shrinkage Confidence Procedures

TL;DR

This paper explores shrinkage techniques to improve multivariate normal confidence procedures, utilizing Bayesian and empirical Bayesian methods to achieve better confidence set estimation.

Contribution

It provides a comprehensive review of developments in confidence set estimation using shrinkage, including analytic and numerical domination results.

Findings

Shrinkage methods can outperform traditional confidence procedures.

Bayesian and empirical Bayesian approaches are effective in confidence set estimation.

Numerical results support the superiority of shrinkage-based confidence sets.

Abstract

The possibility of improving on the usual multivariate normal confidence was first discussed in Stein (1962). Using the ideas of shrinkage, through Bayesian and empirical Bayesian arguments, domination results, both analytic and numerical, have been obtained. Here we trace some of the developments in confidence set estimation.