A Note on Improved Multivariate Normal Mean Estimation With Unknown Covariance When p Is Greater Than n
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929396255817728 |
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| author | Foroushani, Arash A. Nkurunziza, Severien |
| author_facet | Foroushani, Arash A. Nkurunziza, Severien |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_13140 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Note on Improved Multivariate Normal Mean Estimation With Unknown Covariance When p Is Greater Than n Foroushani, Arash A. Nkurunziza, Severien Statistics Theory 62C20 (Primary) 62H12 (Secondary) 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. |
| title | A Note on Improved Multivariate Normal Mean Estimation With Unknown Covariance When p Is Greater Than n |
| topic | Statistics Theory 62C20 (Primary) 62H12 (Secondary) |
| url | https://arxiv.org/abs/2311.13140 |