Baranchick-type Estimators of a Multivariate Normal Mean Under the General Quadratic Loss Function

Hamdaoui, Abdenour; Benkhaled, Abdelkader; Terbeche, Mekki

doi:10.17516/1997-1397-2020-13-5-608-621

Cited by 5 publications

(2 citation statements)

References 5 publications

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“…We recall the form of the James-Stein estimator δ JS given in (5). Its risk function associated to the balanced squared error loss function L ω is given by the formula (6).…”

Section: Simulation Resultsmentioning

confidence: 99%

“…This latter has become a very important technique for modelling data and provides useful techniques for combining data from various sources. Recent studies, in the context of shrinkage estimation, include Amin et al [1], Yuzba et al [15] and Hamdaoui et al [6]. Benkhaled and Hamdaoui [3], have considered two forms of shrinkage estimators of the mean θ of a multivariate normal distribution X ∼ N p (θ, σ 2 I p ) where σ 2 is unknown and estimated by the statistic…”

Section: Introductionmentioning

confidence: 99%

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Polynomials shrinkage estimators of a multivariate normal mean

Benkhaled¹,

Terbeche²,

Hamdaoui³

2021

Preprint

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In this work, the estimation of the multivariate normal mean by different classes of shrinkage estimators is investigated. The risk associated with the balanced loss function is used to compare two estimators. We start by considering estimators that generalize the James-Stein estimator and show that these estimators dominate the maximum likelihood estimator (MLE), therefore are minimax, when the shrinkage function satisfies some conditions. Then, we treat estimators of polynomial form and prove the increase of the degree of the polynomial allows us to build a better estimator from the one previously constructed.

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“…We recall the form of the James-Stein estimator δ JS given in (5). Its risk function associated to the balanced squared error loss function L ω is given by the formula (6).…”

Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Polynomials shrinkage estimators of a multivariate normal mean

Benkhaled¹,

Terbeche²,

Hamdaoui³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

On shrinkage estimators improving the positive part of James-Stein estimator

Hamdaoui¹

2021

Demonstratio Mathematica

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In this work, we study the estimation of the multivariate normal mean by different classes of shrinkage estimators. The risk associated with the quadratic loss function is used to compare two estimators. We start by considering a class of estimators that dominate the positive part of James-Stein estimator. Then, we treat estimators of polynomial form and prove if we increase the degree of the polynomial we can build a better estimator from the one previously constructed. Furthermore, we discuss the minimaxity property of the considered estimators.

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A study of minimax shrinkage estimators dominating the James-Stein estimator under the balanced loss function

et al. 2022

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One of the most common challenges in multivariate statistical analysis is estimating the mean parameters. A well-known approach of estimating the mean parameters is the maximum likelihood estimator (MLE). However, the MLE becomes inefficient in the case of having large-dimensional parameter space. A popular estimator that tackles this issue is the James-Stein estimator. Therefore, we aim to use the shrinkage method based on the balanced loss function to construct estimators for the mean parameters of the multivariate normal (MVN) distribution that dominates both the MLE and James-Stein estimators. Two classes of shrinkage estimators have been established that generalized the James-Stein estimator. We study their domination and minimaxity properties to the MLE and their performances to the James-Stein estimators. The efficiency of the proposed estimators is explored through simulation studies.

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Baranchick-type Estimators of a Multivariate Normal Mean Under the General Quadratic Loss Function

Cited by 5 publications

References 5 publications

Polynomials shrinkage estimators of a multivariate normal mean

Polynomials shrinkage estimators of a multivariate normal mean

On shrinkage estimators improving the positive part of James-Stein estimator

A study of minimax shrinkage estimators dominating the James-Stein estimator under the balanced loss function

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