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