Inadmissibility of the corrected Akaike information criterion

TL;DR

This paper demonstrates that the corrected Akaike information criterion, while unbiased for expected Kullback--Leibler discrepancy, is inadmissible for estimating the discrepancy itself, and proposes improved estimators.

Contribution

It reveals the inadmissibility of the corrected AIC for estimating the Kullback--Leibler discrepancy and introduces better estimators for reduced-rank cases.

Findings

Corrected AIC is inadmissible for the discrepancy itself.

Proposed estimators perform well in reduced-rank scenarios.

Numerical experiments confirm the effectiveness of new estimators.

Abstract

For the multivariate linear regression model with unknown covariance, the corrected Akaike information criterion is the minimum variance unbiased estimator of the expected Kullback--Leibler discrepancy. In this study, based on the loss estimation framework, we show its inadmissibility as an estimator of the Kullback--Leibler discrepancy itself, instead of the expected Kullback--Leibler discrepancy. We provide improved estimators of the Kullback--Leibler discrepancy that work well in reduced-rank situations and examine their performance numerically.