Generalized Bayesian shrinkage and wavelet estimation of location parameter for spherical distribution under balance-type loss: Minimaxity and admissibility

Karamikabir, Hamid; Afshari, Mahmoud

doi:10.1016/j.jmva.2019.104583

Cited by 18 publications

(5 citation statements)

References 18 publications

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“…where 􏽢 β and 􏽢 c are defned in equations ( 19) and (32), respectively, and the parameter δ behaves like c in equation (21). Te analogous technique used in the proof of Proposition 2 leads to the following proposition.…”

mentioning

confidence: 81%

“…is defned in equation ( 5) and its risk function under the BLF ℓ ω is given in equation ( 6), and the estimators T (2) 􏽢 β,JS+ (Y), T (3) 􏽢 c,JS+ (Y), and T (4) 􏽢 δ,JS+ (Y) are defned, respectively, in equations (7), (21), and (34…”

Section: Simulation Studiesmentioning

confidence: 99%

“…Zellner [16] extended the problem of estimating the multivariate normal mean in large dimension, and then he suggested the BLF that generalizes the quadratic loss function. Te published papers in this direction include Sanjari Farsipour and Asgharzadeh [17], Selahattin and Issam [18], Nimet and Selahattin [19], Lahoucine et al [20], Karamikabir and Afsahri [21], and Karamikabir et al [22].…”

Section: Introductionmentioning

confidence: 99%

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On Some Classes of Estimators Derived from the Positive Part of James–Stein Estimator

Hamdaoui

Benkhaled

Alshahrani

et al. 2023

Journal of Mathematics

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This work consists of developing shrinkage estimation strategies for the multivariate normal mean when the covariance matrix is diagonal and known. The domination of the positive part of James–Stein estimator (PPJSE) over James–Stein estimator (JSE) relative to the balanced loss function (BLF) is analytically proved. We introduce a new class of shrinkage estimators which ameliorate the PPJSE, and then we construct a series of polynomial shrinkage estimators which improve the PPJSE; also, any estimator of this series can be ameliorated by adding to it a new term of higher degree. We end this paper by simulation studies which confirm the performance of the suggested estimators.

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mentioning

confidence: 81%

Section: Simulation Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Some Classes of Estimators Derived from the Positive Part of James–Stein Estimator

Hamdaoui

Benkhaled

Alshahrani

et al. 2023

Journal of Mathematics

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show abstract

“…For more details about this loss see Jafari Jozani et al [7], Zinodiny et al [17] and Karamikabir and Afsahri [9].…”

Section: Resultsmentioning

confidence: 99%

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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“…There is much room for meta-analyzing bivariate and multivariate responses [47][48][49][50][51][52][53][54][55][56]. Multivariate shrinkage estimators of multivariate restricted and unrestricted normal means, such as those in [57][58][59][60], can be considered for this extension.…”

Section: Conclusion and Future Extensionsmentioning

confidence: 99%

meta.shrinkage: An R Package for Meta-Analyses for Simultaneously Estimating Individual Means

et al. 2022

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Meta-analysis is an indispensable tool for synthesizing statistical results obtained from individual studies. Recently, non-Bayesian estimators for individual means were proposed by applying three methods: the James–Stein (JS) shrinkage estimator, isotonic regression estimator, and pretest (PT) estimator. In order to make these methods available to users, we develop a new R package meta.shrinkage. Our package can compute seven estimators (named JS, JS+, RML, RJS, RJS+, PT, and GPT). We introduce this R package along with the usage of the R functions and the “average-min-max” steps for the pool-adjacent violators algorithm. We conduct Monte Carlo simulations to validate the proposed R package to ensure that the package can work properly in a variety of scenarios. We also analyze a data example to show the ability of the R package.

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Generalized Bayesian shrinkage and wavelet estimation of location parameter for spherical distribution under balance-type loss: Minimaxity and admissibility

Cited by 18 publications

References 18 publications

On Some Classes of Estimators Derived from the Positive Part of James–Stein Estimator

On Some Classes of Estimators Derived from the Positive Part of James–Stein Estimator

Polynomials shrinkage estimators of a multivariate normal mean

meta.shrinkage: An R Package for Meta-Analyses for Simultaneously Estimating Individual Means

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