English

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

Statistics Theory 2024-06-25 v2 Statistics Theory

Abstract

In this paper, we highlight a major error in the proofs of the important results of [D.Ch\'etelat 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.

Keywords

Cite

@article{arxiv.2311.13140,
  title  = {A Note on Improved Multivariate Normal Mean Estimation With Unknown Covariance When p Is Greater Than n},
  author = {Arash A. Foroushani and Severien Nkurunziza},
  journal= {arXiv preprint arXiv:2311.13140},
  year   = {2024}
}
R2 v1 2026-06-28T13:28:10.986Z