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In this paper, we highlight a major error in the proofs of the importantresults of [D.Ch\'etelat and M. T. Wells(2012). Improved Multivariate NormalMean Estimation with Unknown Covariance when p is Greater than n. The Annals ofStatistics, Vol. 40, No.6, 3137--3160]. In particular, the proofs of some oftheir main results are based on Theorem 2 whose proof needs to be revisited.More precisely, there are some major mistakes in the derivation of thisimportant result. Further, under a very realistic assumption about the rank ofthe estimator of the variance-covariance matrix, we correct the proof of thequoted result.

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