Bayes minimax estimation of the multivariate normal mean vector under quadratic loss functions

Zinodiny, S.; Rezaei, Satar; Arjmand, Omid Naghshineh; Nadarajah, Saralees

doi:10.1016/j.spl.2013.05.021

Cited by 9 publications

(3 citation statements)

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“…The covariance matrix in the prior (21) is positive definite for 0 < λ, ξ < 1. It is noted that when Q i = V −1 i , integrating out the prior (12) with respect to ν leads to the same density function as in (21) with the constraint ξ < λ. The prior distribution (21) does not have to assume this constraint.…”

Section: Hierarchical Bayes Minimax Estimatorsmentioning

confidence: 97%

“…Remark 1. When ν = 0, the prior distribution (3) was treated in [1,12]. There exists a nonsingular matrix…”

Section: Shrinkage Toward the Pooled Estimatormentioning

confidence: 99%

“…Although a natural prior is a hierarchical prior based on (12), the minimaxity of the resulting Bayes estimator is difficult to show, because the integrals with respect to ξ and λ are taken over the constraint ξ < λ. Instead of ( 12), we here consider the following prior distribution for M = (µ 1 , .…”

Section: Hierarchical Bayes Minimax Estimatorsmentioning

confidence: 99%

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Bayesian simultaneous estimation for means in k-sample problems

Imai¹,

Kubokawa²,

Ghosh³

2019

Journal of Multivariate Analysis

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This paper is concerned with the simultaneous estimation of k population means when one suspects that the k means are nearly equal. As an alternative to the preliminary test estimator based on the test statistics for testing hypothesis of equal means, we derive Bayesian and minimax estimators which shrink individual sample means toward a pooled mean estimator given under the hypothesis. It is shown that both the preliminary test estimator and the Bayesian minimax shrinkage estimators are further improved by shrinking the pooled mean estimator. The performance of the proposed shrinkage estimators is investigated by simulation.

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Section: Hierarchical Bayes Minimax Estimatorsmentioning

confidence: 97%

“…Remark 1. When ν = 0, the prior distribution (3) was treated in [1,12]. There exists a nonsingular matrix…”

Section: Shrinkage Toward the Pooled Estimatormentioning

confidence: 99%