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.
Funding Statement
This work was supported by JSPS KAKENHI Grant Numbers 19K20220, 21H05205, 22K17865 and JST Moonshot Grant Number JPMJMS2024.
Acknowledgments
The author thanks the associate editor and referees for valuable comments.
Citation
Takeru Matsuda. "Inadmissibility of the corrected Akaike information criterion." Bernoulli 30 (2) 1416 - 1440, May 2024. https://doi.org/10.3150/23-BEJ1638
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