Preliminary test and Stein-type shrinkage ridge estimators in robust regression

Norouzirad, Mina; Arashi, Mohammad

doi:10.1007/s00362-017-0899-3

Cited by 21 publications

(8 citation statements)

References 32 publications

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“…In many cases, regression models are extended by regularization due to at least one of the following aspects: (i) allow for high-dimensional inference (Neykov et al 2014), (ii) perform variable selection (Zhang and Xiang 2015;Yang et al 2018), and (iii) deal with multicollinearity (Norouzirad and Arashi 2019). Apart from these common applications, Bertsimas and Copenhaver (2018) provided novel insights by showing that (2) and ( 3) are equivalent if g is a semi-norm and h is a norm.…”

Section: Introductionmentioning

confidence: 99%

The generalized equivalence of regularization and min–max robustification in linear mixed models

et al. 2021

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The connection between regularization and min–max robustification in the presence of unobservable covariate measurement errors in linear mixed models is addressed. We prove that regularized model parameter estimation is equivalent to robust loss minimization under a min–max approach. On the example of the LASSO, Ridge regression, and the Elastic Net, we derive uncertainty sets that characterize the feasible noise that can be added to a given estimation problem. These sets allow us to determine measurement error bounds without distribution assumptions. A conservative Jackknife estimator of the mean squared error in this setting is proposed. We further derive conditions under which min-max robust estimation of model parameters is consistent. The theoretical findings are supported by a Monte Carlo simulation study under multiple measurement error scenarios.

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Section: Introductionmentioning

confidence: 99%

The generalized equivalence of regularization and min–max robustification in linear mixed models

et al. 2021

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“…Hossain et al 16 considered shrinkage, pretest, and penalty estimators in generalized linear models when there are many potential predictors. For related works, see the works of Griffin and Brown, 17 Arabi Belaghi et al, 18 Arashi and Roozbeh, 19,20 Shah et al, 21 Ginestet et al, 22 Norouzirad and Arashi, 23,24 Yüzbaşı and Ahmed, 25 and Reangsephet et al 26 Recently, Norouzirad et al 27 developed shrinkage and penalized estimators in weighted least absolute deviations regression models.…”

Section: Methodsmentioning

confidence: 99%

Stein‐type shrinkage estimators in gamma regression model with application to prostate cancer data

Mandal

Belaghi

Mahmoudi

et al. 2019

Statistics in Medicine

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Funding information Natural Sciences and Engineering Research Council (NSERC) of CanadaGamma regression is applied in several areas such as life testing, forecasting cancer incidences, genomics, rainfall prediction, experimental designs, and quality control. Gamma regression models allow for a monotone and no constant hazard in survival models. Owing to the broad applicability of gamma regression, we propose some novel and improved methods to estimate the coefficients of gamma regression model. We combine the unrestricted maximum likelihood (ML) estimators and the estimators that are restricted by linear hypothesis, and we present Stein-type shrinkage estimators (SEs). We then develop an asymptotic theory for SEs and obtain their asymptotic quadratic risks. In addition, we conduct Monte Carlo simulations to study the performance of the estimators in terms of their simulated relative efficiencies. It is evident from our studies that the proposed SEs outperform the usual ML estimators. Furthermore, some tabular and graphical representations are given as proofs of our assertions. This study is finally ended by appraising the performance of our estimators for a real prostate cancer data. KEYWORDS asymptotic quadratic risk, gamma regression, positive-part Stein-type shrinkage estimator, prostate cancer, relative efficiency, Stein-type shrinkage estimator 4310

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“…Recent studies, in the context of shrinkage RR, include Roozbeh (), Roozbeh & Arashi (), Yüzbaşı & Ejaz Ahmed (), and Yüzbaşı et al (), where they developed ridge‐type shrinkage estimations in partial linear models. Norouzirad & Arashi () studied the shrinkage ridge estimators in robust regression. Also, Wu & Asar () considered a weighted stochastic restricted ridge estimator in such models.…”

Section: Introductionmentioning

confidence: 99%

Shrinkage Estimation Strategies in Generalised Ridge Regression Models: Low/High‐Dimension Regime

Yüzbaşı

Arashi

Ahmed

2020

Int Statistical Rev

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Summary In this study, we suggest pretest and shrinkage methods based on the generalised ridge regression estimation that is suitable for both multicollinear and high‐dimensional problems. We review and develop theoretical results for some of the shrinkage estimators. The relative performance of the shrinkage estimators to some penalty methods is compared and assessed by both simulation and real‐data analysis. We show that the suggested methods can be accounted as good competitors to regularisation techniques, by means of a mean squared error of estimation and prediction error. A thorough comparison of pretest and shrinkage estimators based on the maximum likelihood method to the penalty methods. In this paper, we extend the comparison outlined in his work using the least squares method for the generalised ridge regression.

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Preliminary test and Stein-type shrinkage ridge estimators in robust regression

Cited by 21 publications

References 32 publications

The generalized equivalence of regularization and min–max robustification in linear mixed models

The generalized equivalence of regularization and min–max robustification in linear mixed models

Stein‐type shrinkage estimators in gamma regression model with application to prostate cancer data

Shrinkage Estimation Strategies in Generalised Ridge Regression Models: Low/High‐Dimension Regime

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