A penalized approach to covariate selection through quantile regression coefficient models

Sottile, Gianluca; Frumento, Paolo; Chiodi, Marcello; Bottai, Matteo

doi:10.1177/1471082x19825523

Cited by 10 publications

(8 citation statements)

References 35 publications

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“…2; it is therefore possible, starting from these partial benchmark reference curves, define intermediate benchmarks useful in the short and medium term. Sottile et al (2019) suggested a penalized method that can address the selection of covariates in the QRCM modelling framework "directly on the parameters of the conditional quantile function [and] using information on all quantiles".…”

Section: Frontier Qrcm Modelmentioning

confidence: 99%

Stochastic frontier estimation through parametric modelling of quantile regression coefficients

2022

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Stochastic frontiers are a very popular tool used to compare production units in terms of efficiency. The parameters of this class of models are usually estimated through the use of the classic maximum likelihood method even, in the last years, some authors suggested to conceive and estimate the productive frontier within the quantile regression framework. The main advantages of the quantile approach lie in the weaker assumptions about data distribution and in the greater robustness to the presence of outliers respect to the maximum likelihood approach. However, empirical evidence and theoretical contributions have highlighted that the quantile regression applied to the tails of the conditional distribution, namely the frontiers, suffers from instability in estimates and needs specific tools and approaches. To avoid this limitation, we propose to model the parameters of the stochastic frontier as a function of the quantile in order to smooth its trend and, consequently, reduce its instability. The approach has been illustrated using real data and simulated experiments confirming the good robustness and efficiency properties of the proposed method.

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Section: Frontier Qrcm Modelmentioning

confidence: 99%

Stochastic frontier estimation through parametric modelling of quantile regression coefficients

2022

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“…Because the number of components is unknown a-priori, following Pan and Shen (2007); Städler et al (2010) and Sottile et al (2020), to account for shrinkage we select G by employing the modified Bayesian Information Criterion (BIC) (Schwarz et al, 1978): …”

Section: Simulation Studymentioning

confidence: 99%

“…to allow for skewed data and b i ∼ T 2 (0, ) with degrees of freedom.We assumed the following true values for the model parameters: γ = (−1.5, 2.5, 1), β = (2, 0.5, −1) and = 0of components is unknown a-priori, following Pan and Shen (2007); St ädler et al (2010) andSottile et al (2020), to account for shrinkage we select G by employing the modified Bayesian Information Criterion (BIC)(Schwarz et al, 1978): BIC = −2 log(L) + ν f log(N), (4.4)…”

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confidence: 99%

Two-part quantile regression models for semi-continuous longitudinal data: A finite mixture approach

Maruotti

Merlo

Petrella

2021

Statistical Modelling

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This article develops a two-part finite mixture quantile regression model for semi-continuous longitudinal data. The proposed methodology allows heterogeneity sources that influence the model for the binary response variable to also influence the distribution of the positive outcomes. As is common in the quantile regression literature, estimation and inference on the model parameters are based on the asymmetric Laplace distribution. Maximum likelihood estimates are obtained through the EM algorithm without parametric assumptions on the random effects distribution. In addition, a penalized version of the EM algorithm is presented to tackle the problem of variable selection. The proposed statistical method is applied to the well-known RAND Health Insurance Experiment dataset which gives further insights on its empirical behaviour.

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“…SCAD and MCP type penalties also mitigate the estimation bias of the LASSO. Sherwood and Maidman, 2020 and Sottile et al, 2020 give suites of penalization methods for variable selection in quantile regression.…”

Section: Variable Selection In Quantile Regressionmentioning

confidence: 99%

Mixed effect modelling and variable selection for quantile regression

Bar

Booth

Wells

2021

Statistical Modelling

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It is known that the estimating equations for quantile regression (QR) can be solved using an EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent generalized inverse-Gaussian variables. This fact is exploited here to extend QR to allow for random effects in the linear predictor. Convergence of the algorithm in this setting is established by showing that it is a generalized alternating minimization (GAM) procedure. Another modification of the EM algorithm also allows us to adapt a recently proposed method for variable selection in mean regression models to the QR setting. Simulations show that the resulting method significantly outperforms variable selection in QR models using the lasso penalty. Applications to real data include a frailty QR analysis of hospital stays, and variable selection for age at onset of lung cancer and for riboflavin production rate using high-dimensional gene expression arrays for prediction.

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A penalized approach to covariate selection through quantile regression coefficient models

Cited by 10 publications

References 35 publications

Stochastic frontier estimation through parametric modelling of quantile regression coefficients

Stochastic frontier estimation through parametric modelling of quantile regression coefficients

Two-part quantile regression models for semi-continuous longitudinal data: A finite mixture approach

Mixed effect modelling and variable selection for quantile regression

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