Selection of Variables in Quantile Regression (Linear Lasso- Goal Programming)
Keywords:Quantile Regression - Linear Lasso- Selection of Variables - goal programming - estimated risk - relative estimated risk
Quantile regression is a statistical technique intended to estimate, and conduct inference about the conditional quantile functions. Since Koenker and Bassett (1978) introduced quantile regression, which models conditional quantiles as functions of predictors. The quantile regression can give complete information about the relationship between the response variable and covariates on the entire conditional distribution, and has no distributional assumption about the error term in the model. The study evaluates the performance of three methods; two methods of linear programming linear lasso ( 12L1"> -Lasso, 12L2"> -Lasso) and one method of Goal programming. The three methods are used to select the best subset of variables and estimate the parameters of the quantile regression equation when four error distributions, with two different sample sizes and two different parameters for each error distribution. The study found that the estimated risk and relative estimated risk which produced from Goal programming method is less than ER and ERE of ( 12L1"> -Lasso and 12L2"> -Lasso methods.
Alhamzawi, R., Yu, K. and Benoit, T. (2012). Bayesian adaptive lasso quantile regression. Statistical Modelling, 12(3) , 279-297.
Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004). Least angle regression. The Annals of Statistics, 32, 407-499.
Fan, J. and Lv, J. (2010). Aselective overview of variable selection in high dimensional feature space. Statistica Sinica, 20, 101-148.
Ismail, A. R. (2003). Curve fitting for data with outliers using fuzzy linear programming. Unpublished Ph.D. thesis, Faculty of Commerce, Al-Azhar University-Girls' Branch.
Koenker, R. and Bassett, G. (1978). Regression quantiles. Econometrica, 46, 33-50.
Li, Q., Xi, R. and Lin, N. (2010). Bayesian regularized quantile regression. Bayesian Analysis, 5, 1-24.
Li, Y. and Zhu, J. (2008). L1-Normal quantile regression. Journal of Computational and Graphical Statistics, 17, 163-185.
Miller, A. (1990). Subset selection regression. Chapmanand Hall.
Osborne, M., Presnell, B. and Turlach, B. (2000). On the Lasso and its dual. Journal of Computational and Graphical Statistics, 9, 319-337.
Schmidt, E., Berg, M., Fried, L. and Murphy, k. (2007). Group sparsity via linear time projection. Technical report. TR, Department of Computer Science, University of British Columba, Vancouver, July.
Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society, Series B, 58, 267-288.
Zou, H. and Yuan, M. (2008). Regularized simultaneous model selection in multiple quantiles regression. Computational Statistics and Data Analysis, 52, 5296-5304.
How to Cite
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.