Proposing Shrinkage Estimator of MCP and Elastic-Net penalties in Quantile Regression Model.

Abstract

In some studies, there is a need to estimate the conditional distribution of the response variable at different points, and this is not available in linear regression. The alternative procedure to deal with these problems is quantile regression. In this research, a new estimator for estimating and selecting variables is proposed in the quantile regression model. A new estimator was combines two estimators Minimax Concave Penalty (MCP) and Elastic-Net called shrinkage estimator. It was compared with estimators (Minimax Concave Penalty (MCP) and Elastic-Net) by using simulation and based on Mean Square Error (MSE) and measures of sparsity False Positive Rate (FPR) and False negative rate (FNR ). We concluded that the proposed method is the best in terms of estimation and selection of variables