Model-free Feature Screening and False Discovery Control for High-dimensional Quantile Regressions

原文摘要

High-dimensional quantile regressions are powerful tools for capturing the diverse relationships between predictors and response variables across different quantile levels. However, existing feature screening methods for quantile regressions often rely on restrictive model assumptions, limiting their applicability in complex data settings. In this paper, we propose a novel model-free feature screening framework for high-dimensional quantile regressions, leveraging a novel statistical measure called Copula Quantile Dependence. This measure quantifies the functional dependence between predictors and the response variable at a given quantile level without requiring a predefined model structure. Building on this concept, we develop the Quantile Copula-based Screening (QC-Screen) method, which ranks features based on their Copula Quantile Dependence values and selects the most informative ones. We also introduce a data-driven procedure named QC-FDR to control the False Discovery Rate (FDR) while ensuring the inclusion of significant predictors. We establish the theoretical properties of QC-Screen, proving its sure screening and rank consistency properties, and demonstrate that QC-FDR asymptotically controls FDR at the desired level. Extensive simulations and a real-world economic data analysis confirm the superior empirical performance of QC-Screen and QC-FDR, highlighting their effectiveness in high-dimensional quantile regressions.

摘要来源：OpenAlex