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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of multivariate analysis 2011-10, Vol.102 (9), p.1256-1262
Hauptverfasser: Zinodiny, S., Strawderman, W.E., Parsian, A.
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
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.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2011.04.008