Minimax estimation of the mean of the multivariate normal distribution

作者：Zinodiny S; Rezaei S^*; Nadarajah S

来源：Communications in Statistics - Theory and Methods, 2017, 46(3): 1422-1432.

DOI：10.1080/03610926.2015.1019146

• Bayes estimation
• Extended balanced loss function
• Extended reflected normal loss function
• Minimax estimation
• Multivariate normal mean
• 62E99

The problem of estimating the mean vector theta of a multivariate normal distribution with known covariance matrix 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 ofminimax estimators of 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.

• 出版日期2017