Bayes minimax estimation of the multivariate normal mean vector for the case of common unknown variance
We investigate the problem of estimating the mean vector θ of a multivariate normal distribution with covariance matrix σ 2 I p , when σ 2 is unknown, and where the loss function is ‖ δ − θ ‖ 2 σ 2 . We find a large class of (proper and generalized) Bayes minimax estimators of θ , and show that the...
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Veröffentlicht in: | Journal of multivariate analysis 2011-10, Vol.102 (9), p.1256-1262 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
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Zusammenfassung: | We investigate the problem of estimating the mean vector
θ
of a multivariate normal distribution with covariance matrix
σ
2
I
p
, when
σ
2
is unknown, and where the loss function is
‖
δ
−
θ
‖
2
σ
2
. We find a large class of (proper and generalized) Bayes minimax estimators of
θ
, and show that the result of Strawderman (1973)
[8] is a special case of our result. Since a large subclass of the estimators found are proper Bayes, and therefore admissible, the class of admissible minimax estimators is substantially enlarged as well. |
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ISSN: | 0047-259X 1095-7243 |
DOI: | 10.1016/j.jmva.2011.04.008 |