Behavior of Lasso Quantile Regression with Small Sample Sizes

Quantile regression is a statistical technique intended to estimate, and conduct inference about the conditional quantile functions. Just as the classical linear regression methods estimate models for conditional mean function, quantile regression offers a mechanism for estimating models for conditional median function, and the full range of other conditional quantile functions. In this paper describe, compare, and apply the two quantile regression (L1-Lasso, L2-Lasso) suggested approaches. The two quantile regression suggested approaches used to select the best subset of variables and estimate the parameters of the quantile regression equation when small sample sizes are used. The aim of this study is to study the behavior of L1Lasso and L2 -Lasso quantile regression method when small sample sizes are generated. Simulations show that the proposed approaches are very competitive in terms of variable selection, estimation accuracy and efficient when small sample sizes are used. All results showed superiority of L1 -Lasso compared with L2 -Lasso linear programming methods. Keywords—Quantile Regression – Small Sample size – Selection of Variables estimated risk – relative estimated risk.