A Note on Improved Multivariate Normal Mean Estimation With Unknown Covariance When p Is Greater Than n

2023/11/22 by Arash A. Foroushani, Foroushani, Arash A., Sévérien Nkurunziza +1
Decision Sciences · Mathematics · #62C20 (Primary) 62H12 (Secondary) #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #FOS: Mathematics #Mathematical Inequalities and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2311.13140

openalex publication_date 2023/11/22 · openalex created_date 2023/11/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we highlight a major error in the proofs of the important results of [D.Chételat and M. T. Wells(2012). Improved Multivariate Normal Mean Estimation with Unknown Covariance when p is Greater than n. The Annals of Statistics, Vol. 40, No.6, 3137--3160]. In particular, the proofs of some of their main results are based on Theorem 2 whose proof needs to be revisited. More precisely, there are some major mistakes in the derivation of this important result. Further, under a very realistic assumption about the rank of the estimator of the variance-covariance matrix, we correct the proof of the quoted result.

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