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<p>Sparse penalized quantile regression, as an effective tool, not only enables robust variable selection but also provides reliable estimation results in high-dimensional data analysis. High-dimensional data often come with high correlations among variables, posing challenges for analytical methods, which should ideally be able to effectively address this issue. To tackle this problem, this paper proposes an adaptive elastic net penalized quantile regression method (Q-AEnet) that combines the advantages of the quantile loss function and adaptive elastic net penalty. Under certain regularity conditions, the proposed method exhibits the oracle property, which means it can accurately identify the true model, implying that the model can achieve ideal prediction or estimation results based on certain optimality criteria. Furthermore, the asymptotic normal distribution of non-zero coefficients is derived. Additionally, to efficiently compute the adaptive elastic net penalized quantile regression, we use a generalized coordinate descent (GCD) algorithm based on a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\delta \)</EquationSource> </InlineEquation> smoothing loss function. Through numerical simulation studies and real data analysis, the proposed Q-AEnet method exhibits superior performance in finite sample scenarios with highly correlated covariates.</p>

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Adaptive elastic net penalized high-dimensional quantile regression models with generalized coordinate descent algorithm

  • 期刊论文

  • 发表日期：

    2026年1月17日

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  • Yiping Yang,
  • Liugen Xue,
  • Gaorong Li

摘要

Sparse penalized quantile regression, as an effective tool, not only enables robust variable selection but also provides reliable estimation results in high-dimensional data analysis. High-dimensional data often come with high correlations among variables, posing challenges for analytical methods, which should ideally be able to effectively address this issue. To tackle this problem, this paper proposes an adaptive elastic net penalized quantile regression method (Q-AEnet) that combines the advantages of the quantile loss function and adaptive elastic net penalty. Under certain regularity conditions, the proposed method exhibits the oracle property, which means it can accurately identify the true model, implying that the model can achieve ideal prediction or estimation results based on certain optimality criteria. Furthermore, the asymptotic normal distribution of non-zero coefficients is derived. Additionally, to efficiently compute the adaptive elastic net penalized quantile regression, we use a generalized coordinate descent (GCD) algorithm based on a \(\delta \) smoothing loss function. Through numerical simulation studies and real data analysis, the proposed Q-AEnet method exhibits superior performance in finite sample scenarios with highly correlated covariates.