Bayes minimax estimation of the multivariate normal mean vector for the case of common unknown variance

Abstract

a b s t r a c tWe 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 [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.

A New Class of Bayes Minimax Estimators of the Mean Matrix of a Matrix Variate Normal Distribution

“…Ref. [17] obtained Bayes minimax estimators of the mean for the case of common unknown variance. Ref.…”

An elementary approach for minimax estimation of Bernoulli proportion in the restricted parameter space

“…Besides the maximum likelihood estimator (MLE), the method of moment (MOM), and Bayesian method, another important approach is the minimax estimator that minimizes the maximum risk. The applications of minimax estimators can be found in many fields such as in statistics (Malinovsky and Albert 2015;Yaacoub, Moustakides and Mei 2018;Zinodiny, Strawderman and Parsian 2011), machine learning (Ben-Haim and Eldar 2007), physics Ng, Phuah and Englert 2012) and finance (Chamberlain 2000).…”