On SURE estimates in hierarchical models assuming heteroscedasticity for both levels of a two-level normal hierarchical model

Ghoreishi, Seyed Kamran; Meshkani, M R

doi:10.1016/j.jmva.2014.08.001

Cited by 6 publications

(9 citation statements)

References 8 publications

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“…It is natural to expect that adding one more parameter δ we would have smaller E[l q (θ ,θ )] in comparison to our pervious work, Ghoreishi and Meshkani (2014).…”

Section: Stein's Unbiased Risk Estimate(sure) Methodsmentioning

confidence: 60%

Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models

Ghoreishi¹,

Mostafavinia²

2015

JSTA

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Empirical Bayes approach is an attractive method for estimating hyperparameters in hierarchical models. But, under the assumption of normality for a multi-level heteroscedastic hierarchical model, which involves several explanatory variables, the analyst may often wonder whether the shrinkage estimators have efficient asymptotic properties in spite of the fact they involve numerous hyperparameters. In this work, we propose a methodology for estimating the hyperparameters whenever one deals with multi-level heteroscedastic hierarchical normal model with several explanatory variables. we investigate the asymptotic properties of the shrinkage estimators when the shrinkage location hyperparameter lies within a suitable interval based on the sample range of the data. Moreover, we show our methodology performs much better in real data sets compared to available approaches.

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“…It is natural to expect that adding one more parameter δ we would have smaller E[l q (θ ,θ )] in comparison to our pervious work, Ghoreishi and Meshkani (2014).…”

Section: Stein's Unbiased Risk Estimate(sure) Methodsmentioning

confidence: 60%

Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models

Ghoreishi¹,

Mostafavinia²

2015

JSTA

Self Cite

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“…see James and Stein [6]; Stein [8]; and Ghoreishi and Meshkani [5]. By applying (5) to the shrinkage estimator (4), the corresponding risk is given by…”

Section: Notations and Definitionsmentioning

confidence: 99%

“…The first and second parts in right hand side are the straightforward results of Theorems 3.1 and 3.2 in Ghoreishi and Meshkani [5], so it is enough to consider the third part,…”

Section: Appendixmentioning

confidence: 99%

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Shrinkage Estimates in a Two-Level Heteroscedastic Hierarchical Normal Models With Linear Trend Mean

Ghoreishi¹

2018

Jour. Stat. Adv. Theory and Appl.

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In heteroscedastic hierarchical normal models, often, the response variable may rather fluctuate around a nonconstant trend than a constant value. In this paper, we assume a linear trend for the second level of a two-level heteroscedastic hierarchical normal model. The empirical Bayes maximum likelihood estimates, Stein's unbiased risk estimates, and Bayesian estimates of the hyperparameters are elicited and the corresponding shrinkage estimates are constructed. The asymptotic properties of the Stein's unbiased risk estimates are illustrated. Since our primary purpose in Bayesian analysis is sampling from the posterior distributions, with assuming some priors for the hyperparameters, the posterior full conditions are given. A real data set is analyzed to demonstrate the proposed methodology. i

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“…Ghoreishi and Meshkani (2014) proposed and developed a class of shrinkage estimators that can be readily applied in a two-level heteroscedastic hierarchical normal models. In this framework, they assumed one or several explanatory variables produce the heteroscedasticty.…”

Section: Introductionmentioning

confidence: 99%

Bayesian analysis of hierarchical heteroscedastic linear models using Dirichlet-Laplace priors

Ghoreishi¹

2017

JSTA

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From practical point of view, in a two-level hierarchical model, the variance of second-level usually has a tendency to change through sub-populations. The existence of this kind of local (or intrinsic ) heteroscedasticity is a major concern in the application of statistical modeling. The main purpose of this study is to construct a Bayesian methodology via shrinkage priors in order to estimate the interesting parameters under local heteroscedasticity. The suggested methodology for this issue is to use of a class of the local-global shrinkage priors, called Dirichlet-Laplace priors. The optimal posterior concentration and straightforward posterior computation are the appealing properties of these priors. Two real data sets are analyzed to illustrate the proposed methodology.

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On SURE estimates in hierarchical models assuming heteroscedasticity for both levels of a two-level normal hierarchical model

Cited by 6 publications

References 8 publications

Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models

Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models

Shrinkage Estimates in a Two-Level Heteroscedastic Hierarchical Normal Models With Linear Trend Mean

Bayesian analysis of hierarchical heteroscedastic linear models using Dirichlet-Laplace priors

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