Robust Variable Selection for Quantile Regression: Application to Daily Demand Forecasting Orders Data

Zainab S  Alsaadi

Zainab S Alsaadi Department of Studies and Planning, Presidency of the University, University of Al-Qadisiyah, Al-Qadisiyah, Iraq

Keywords: Quantile Regression, Robust Variable Selection, Elastic Net, MCP Penalty, Demand Forecasting

Abstract

This paper proposes two robust variable selection methods within the quantile regression framework: Robust Elastic Net Quantile Regression (REN-QR) and Robust MCP Quantile Regression (R-MCP-QR). These approaches integrate adaptive penalization with GM-type weighting schemes to improve estimation accuracy and feature selection under high-dimensional and contaminated conditions. Through extensive simulation studies, the proposed methods demonstrate superior performance in terms of mean squared error (MSE), true positive rate (TPR), and false positive rate (FPR) compared to classical penalized quantile regression techniques. Furthermore, the application to a real-world dataset on daily demand forecasting orders confirms their effectiveness in capturing relevant predictors while maintaining robustness against outliers. The results highlight the utility of robust penalized quantile regression for accurate and interpretable modeling in complex data environments.

References

S. A. AL-Sabbah and S. H. Raheem, "Use Bayesian adaptive Lasso for Tobit regression with real data," International Journal of Agricultural & Statistical Sciences, vol. 17, 2021.

S. A. AL-Sabbah, L. A. Mohammed, and S. H. Raheem, "Sliced inverse regression (SIR) with robust group lasso," International Journal of Agricultural & Statistical Sciences, vol. 17, no. 1, 2021.

B. K. M. S. H. R. T. R. Dikheel, "Sliced inverse regression (SIR) via group lasso," Al-Rafidain University College for Sciences, vol. 46, no. 1, pp. 505–512, 2021.

J. Fan and R. Li, "Variable selection via nonconcave penalized likelihood and its oracle properties," J. Am. Stat. Assoc., vol. 96, no. 456, pp. 1348–1360, 2001.

R. Koenker and G. Bassett, "Regression quantiles," Econometrica, vol. 46, no. 1, pp. 33–50, 1978.

R. Koenker, Quantile Regression. Cambridge University Press, 2005.

Y. Lee and H. Wang, "Penalized quantile regression for high-dimensional data," Statistica Sinica, vol. 25, no. 1, pp. 267–286, 2015.

M. A. Mohammed and S. H. Raheem, "Determine of the most important factors that affect the incidence of heart disease using logistic regression model (Applied study in Erbil Hospital)," Economic Sciences, vol. 15, no. 56, pp. 175–184, 2020.

R. Tibshirani, "Regression shrinkage and selection via the lasso," J. R. Stat. Soc. Ser. B Methodol., vol. 58, no. 1, pp. 267–288, 1996.

H. Wang, G. Li, and G. Jiang, "Robust regression shrinkage and consistent variable selection through the LAD-Lasso," J. Bus. Econ. Stat., vol. 25, no. 3, pp. 347–355, 2013.

Y. Wu and Y. Liu, "Variable selection in quantile regression," Statistica Sinica, vol. 19, no. 2, pp. 801–817, 2009.

C.-H. Zhang, "Nearly unbiased variable selection under minimax concave penalty," Ann. Stat., vol. 38, no. 2, pp. 894–942, 2010.

H. Zou and T. Hastie, "Regularization and variable selection via the elastic net," J. R. Stat. Soc. Ser. B Stat. Methodol., vol. 67, no. 2, pp. 301–320, 2005.

H. Zou and M. Yuan, "Composite quantile regression and the oracle model selection theory," Ann. Stat., vol. 36, no. 3, pp. 1108–1126, 2008.