ESTIMATING AND SELECTING VARIABLES FOR A CONDITIONAL QUANTILE REGRESSION MODEL USING PENALTY FUNCTIONS
DOI:
https://doi.org/10.17977/um066.v6.i6.2026.6Keywords:
quantile regression, Penalized quantile regression, Variable Selection, Lasso Estimator, MCP EstimatorAbstract
Penalised quantile regression is an optimal method for variable selection when confronted with a substantial number of explanatory variables. Certain factors may exert no influence on the response variable, thereby complicating the model and rendering it challenging to interpret. This research concentrates on variable selection utilising punitive functions (lasso) and (MCP), and evaluates them according to the mean square error criterion (MSE) for estimate purposes. Utilising the metrics of false positive rate (FPR) and false negative rate (FNR) to evaluate the estimator's efficacy in variable selection, simulated experiments revealed that the MCP estimator excels in both estimation and variable selection.
References
Amin, M., Song, L., Thorlie, M. A., & Wang, X. (2015). SCAD-penalized quantile regression for high-dimensional data analysis and variable selection. Statistica Neerlandica, 69(3), 212–235.
Buhai, S. (2005). Quantile regression: Overview and selected applications. Ad Astra, 4(4), 1–17.
Fan, J., & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96(456), 1348–1360.
Hao, L., & Naiman, D. Q. (2007). Quantile regression (Vol. 149). Thousand Oaks, CA: Sage Publications.
Hodson, T. O., Over, T. M., & Foks, S. S. (2021). Mean squared error, deconstructed. Journal of Advances in Modeling Earth Systems, 13(12), e2021MS002681.
Ingalls, R. G. (2011). Introduction to simulation. In Proceedings of the 2011 Winter Simulation Conference (pp. 1374–1388). Piscataway, NJ: IEEE.
Koenker, R., & Bassett, G. (1978). Regression quantiles. Econometrica, 46(1), 33–50.
Li, Y., & Zhu, J. (2008). L1-norm quantile regression. Journal of Computational and Graphical Statistics, 17(1), 163–185.
Tibshirani, R. J. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1), 267–288.
Wang, L., Wu, Y., & Li, R. (2012). Quantile regression for analyzing heterogeneity in ultra-high dimension. Journal of the American Statistical Association, 107(497), 214–222.
Wu, Y., & Liu, Y. (2009). Variable selection in quantile regression. Statistica Sinica, 19(2), 801–817.
Yi, C., & Huang, J. (2017). Semismooth Newton coordinate descent algorithm for elastic-net penalized Huber loss regression and quantile regression. Journal of Computational and Graphical Statistics, 26(3), 547–557.
Yousif, A. H., & Housain, W. J. (2021). Atan regularized in quantile regression for high dimensional data. In Journal of Physics: Conference Series (Vol. 1818, No. 1, Article 012098). Bristol, England: IOP Publishing.
Zhang, C. H. (2010). Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics, 38(2), 894–942.
Zhang, J. M., Shi, Q. C., Xu, F. Z., Fu, Y. L., Wang, S. M., Gu, W., ... & Hu, W. P. (2010). False positive rate and false negative rate of the 12-item General Health Questionnaire and related factors. Chinese Mental Health Journal.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Mohammed Ibrahim Zamel
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
3.png)
1.png)
1.png)
