Reversing the Stein Effect

TL;DR

This paper discusses the Reverse Stein Effect, showing that data-dependent shrinkage without reliable prior knowledge can lead to increased estimation error, contrary to traditional shrinkage benefits.

Contribution

It identifies and illustrates the Reverse Stein Effect, highlighting risks of data-dependent shrinkage when prior knowledge is unreliable.

Findings

Data-dependent shrinkage can increase estimation error.

Traditional shrinkage estimators may not always be beneficial.

The Reverse Stein Effect challenges conventional shrinkage assumptions.

Abstract

The Reverse Stein Effect is identified and illustrated: A statistician who shrinks his/her data toward a point chosen without reliable knowledge about the underlying value of the parameter to be estimated but based instead upon the observed data will not be protected by the minimax property of shrinkage estimators such as that of James and Stein, but instead will likely incur a greater error than if shrinkage were not used.