 Minimax estimation of the mean of the multivariate normal distributionS. Zinodiny, S. Rezaei and S. Nadarajah Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 3, 1422-1432 Abstract: The problem of estimating the mean vector θ${\bm \theta }$ of a multivariate normal distribution with known covariance matrix Σ${\bm \Sigma }$ is considered under the extended reflected normal and extended balanced loss functions. We extend the class of minimax estimators obtained by Towhidi and Behboodian (2002) and also by Asgharazadeh and Sanjari Farsipour (2008). The class of estimators derived under the extended balanced loss function includes a special case of estimators obtained by Chung et al. (1999).We introduce a class of minimax estimators of θ${\bm \theta }$ extending Berger’s estimators (1976) and dominating the sample mean in terms of risk under the extended reflected normal and extended balanced loss functions. Using these estimators, we obtain a large class of (proper and generalized) Bayes minimax estimators under the extended balanced loss function and show that the result of Chung and Kim (1998) is a special case of our result. Date: 2017 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:46:y:2017:i:3:p:1422-1432 Ordering information: This journal article can be ordered from DOI: 10.1080/03610926.2015.1019146 Access Statistics for this article Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals |
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