Generalized Bayes minimax estimators of the mean of multivariate normal distribution with unknown variance

Wells, Martin T.; Zhou, Gongfu

doi:10.1016/j.jmva.2008.02.016

Cited by 15 publications

(10 citation statements)

References 21 publications

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“…, from Lemma 4.1 of Wells and Zhou (2008). This shows that our condition (b) is slightly better than (WZ-b) for c > 0.…”

Section: Useful Conditions For the Minimaxity And Simple Examplesmentioning

confidence: 62%

“…Wells and Zhou (2008), hereafter abbreviated by W&Z, recently developed nice results for the minimaxity, and we use their arguments and Proposition 4 to obtain slightly improved conditions for the minimaxity.…”

Section: Minimaxity Of the Generalized Bayes Estimatorsmentioning

confidence: 99%

“…In Section 3, we investigate the minimaxity of the generalized Bayes estimators in similar prior distributions as in Wells and Zhou (2008), who derived the general and nice conditions on the priors. Their interesting point is that for the shrinkage function ψ π (w) of the generalized Bayes estimator, their arguments can handle the case that ψ π (w) is not increasing, but w c ψ π (w) is increasing for some c > 0.…”

Section: Introductionmentioning

confidence: 99%

“…Their interesting point is that for the shrinkage function ψ π (w) of the generalized Bayes estimator, their arguments can handle the case that ψ π (w) is not increasing, but w c ψ π (w) is increasing for some c > 0. In this paper, we reexamine the minimaxity of the generalized Bayes estimators under a similar setup as in Wells and Zhou (2008), and obtain more general and slightly better conditions.…”

Section: Introductionmentioning

confidence: 99%

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Integral Inequality for Minimaxity in the Stein Problem

Kubokawa

2009

JJSS

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In the estimation of a multivariate normal mean, it is shown that the problem of deriving shrinkage estimators improving on the maximum likelihood estimator can be reduced to that of solving an integral inequality. The integral inequality not only provides a more general condition than a conventional differential inequality studied in the literature, but also handles non-differentiable or discontinuous estimators. The paper also gives general conditions on prior distributions such that the resulting generalized Bayes estimators are minimax. Finally, a simple proof for constructing a class of estimators improving on the James-Stein estimator is given based on the integral expression of the risk.

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“…, from Lemma 4.1 of Wells and Zhou (2008). This shows that our condition (b) is slightly better than (WZ-b) for c > 0.…”

Section: Useful Conditions For the Minimaxity And Simple Examplesmentioning

confidence: 62%

Section: Minimaxity Of the Generalized Bayes Estimatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Integral Inequality for Minimaxity in the Stein Problem

Kubokawa

2009

JJSS

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“…Note: A recent paper by Wells and Zhou [11] also derives generalized Bayes estimators in the normal case, some of which have non-monotone shrinkage functions φ (in our notation). The generalized Bayes minimax estimators of Theorem 3.2(ii)…”

Section: Proofmentioning

confidence: 99%

An extended class of minimax generalized Bayes estimators of regression coefficients

Maruyama

Strawderman

2009

Journal of Multivariate Analysis

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a b s t r a c t We derive minimax generalized Bayes estimators of regression coefficients in the general linear model with spherically symmetric errors under invariant quadratic loss for the case of unknown scale. The class of estimators generalizes the class considered in Maruyama and Strawderman [Y. Maruyama, W.E. Strawderman, A new class of generalized Bayes minimax ridge regression estimators, Ann. Statist., 33 (2005) 1753-1770] to include non-monotone shrinkage functions.

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