A comment and erratum on "Excess Optimism: How Biased is the Apparent Error of an Estimator Tuned by SURE?"

TL;DR

This paper corrects an error in a previous work on the bias of SURE-tuned estimators, providing new theoretical guarantees and oracle inequalities for their excess degrees of freedom.

Contribution

It identifies and rectifies an error in prior analysis, enabling accurate bounds on the bias of SURE-tuned linear estimators.

Findings

New guarantees on excess degrees of freedom for SURE-tuned estimators

Oracle inequalities derived for linear estimators

Improved understanding of bias in SURE-based model selection

Abstract

We identify and correct an error in the paper "Excess Optimism: How Biased is the Apparent Error of an Estimator Tuned by SURE?" This correction allows new guarantees on the excess degrees of freedom--the bias in the error estimate of Stein's unbiased risk estimate (SURE) for an estimator tuned by directly minimizing the SURE criterion--for arbitrary SURE-tuned linear estimators. Oracle inequalities follow as a consequence of these results for such estimators.