Shrinkage and penalized estimators in weighted least absolute deviations regression models

Norouzirad, Mina; Hossain, Shakhawat; Arashi, Mohammad

doi:10.1080/00949655.2018.1441415

Cited by 8 publications

(9 citation statements)

References 22 publications

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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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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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“…Therefore, in order to overcome the issue for model (3) when N < v , many recent studies (DeMiguel et al, 2009;Still and Kondor, 2010;Carrasco and Noumon, 2011;Fastrich et al, 2015;Long et al, 2018;Norouzirad et al, 2018) focus on regularization methods such as ridge regression (Hoerl and Kennard, 1970), Least Absolute Shrinkage and Selection Operator (LASSO) (Tibshirani, 2011), Least Angle Regression (LARS) (Efron et al, 2004), Adaptive LASSO (Zou, 2006) and the Dantzig selector (Candes and Tao, 2007). However, all of their estimates are biased giving emphasis to the famous notion of "bias-variance tradeoff", which might over-shrink the coefficients (Radchenko et al, 2011) and perhaps produce inaccurate portfolio weights.…”

Section: Regression With N < V and Its Challengesmentioning

confidence: 99%

Hybrid graphical least square estimation and its application in portfolio selection

Aldahmani

Dai

Zhang

2019

Statistics and Its Interface

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This paper proposes a new regression method based on the idea of graphical models to deal with regression problems with the number of covariates v larger than the sample size N. Unlike the regularization methods such as ridge regression, LASSO and LARS, which always give biased estimates for all parameters, the proposed method can give unbiased estimates for important parameters (a certain subset of all parameters). The new method is applied to a portfolio selection problem under the linear regression framework and, compared to other existing methods, it can assist in improving the portfolio performance by increasing its expected return and decreasing its risk. Another advantage of the proposed method is that it constructs a non-sparse (saturated) portfolio, which is more diversified in terms of stocks and reduces the stock-specific risk. Overall, four simulation studies and a real data analysis from London Stock Exchange showed that our method outperforms other existing regression methods when N < v.

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“…The author of [ 14 ] developed, upon the procedure of [ 19 ] on model selection in composite quantile regression (CQR) and suggested weighted CQR (WCQR), a procedure based on data driven efficient weights, as the former researcher’s equal weight property procedure lacked optimality. To mitigate against the undesirable effects of high leverage points in variable selection in the

estimator (

), the weighted LAD-LASSO (WLAD-LASSO) procedure has been suggested [ 20 , 21 ]. Few variable selection procedures based on WQR have been suggested in the QR regression framework in different settings.…”

Section: Introductionmentioning

confidence: 99%

“…In summary, the motivations of this study are premised on the following: The generalization of WLAD-LASSO [ 20 , 21 ] (in addition, we also include the RIDGE and the E-NET penalties) procedure to the QR framework, i.e., to penalized WQR as each RQ (including the LAD estimator) is a local measure, unlike the LS estimator, which is a global one. Rather than carrying an "omnibus" study of penalized WQR as in [ 20 , 21 ], we carry out a detailed study by distinguishing different types of high leverage points viz., Collinearity influential points which comprise collinearity inducing and collinearity hiding points. High leverage points which are not collinearity influential.…”

Section: Introductionmentioning

confidence: 99%

Variable Selection and Regularization in Quantile Regression via Minimum Covariance Determinant Based Weights

Ranganai

Mudhombo

2020

Entropy

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The importance of variable selection and regularization procedures in multiple regression analysis cannot be overemphasized. These procedures are adversely affected by predictor space data aberrations as well as outliers in the response space. To counter the latter, robust statistical procedures such as quantile regression which generalizes the well-known least absolute deviation procedure to all quantile levels have been proposed in the literature. Quantile regression is robust to response variable outliers but very susceptible to outliers in the predictor space (high leverage points) which may alter the eigen-structure of the predictor matrix. High leverage points that alter the eigen-structure of the predictor matrix by creating or hiding collinearity are referred to as collinearity influential points. In this paper, we suggest generalizing the penalized weighted least absolute deviation to all quantile levels, i.e., to penalized weighted quantile regression using the RIDGE, LASSO, and elastic net penalties as a remedy against collinearity influential points and high leverage points in general. To maintain robustness, we make use of very robust weights based on the computationally intensive high breakdown minimum covariance determinant. Simulations and applications to well-known data sets from the literature show an improvement in variable selection and regularization due to the robust weighting formulation.

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Shrinkage and penalized estimators in weighted least absolute deviations regression models

Cited by 8 publications

References 22 publications

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

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

Hybrid graphical least square estimation and its application in portfolio selection

Variable Selection and Regularization in Quantile Regression via Minimum Covariance Determinant Based Weights

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