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Jackknife model averaging for high-dimensional quantile regression.

Miaomiao Wang1,2,3, Xinyu Zhang2,4, Alan T K Wan5

  • 1School of Chinese Materia Medica, Beijing University of Chinese Medicine, Beijing, China.

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Summary
This summary is machine-generated.

This study introduces a new frequentist model averaging method for high-dimensional quantile regression. The approach effectively handles numerous covariates, outperforming existing penalized regression techniques.

Keywords:
asymptotic optimalityhigh-dimensional quantile regressionmarginal quantile utilitymodel averaging

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Area of Science:

  • Statistics
  • Econometrics
  • Bioinformatics

Background:

  • Quantile regression is crucial for analyzing conditional quantiles.
  • High-dimensional data presents challenges for traditional statistical models.
  • Model averaging offers a robust approach to statistical estimation.

Purpose of the Study:

  • To propose a novel frequentist model averaging method for high-dimensional quantile regression.
  • To integrate covariate dimension reduction with model averaging.
  • To address the lack of combined research in these areas.

Main Methods:

  • Covariate dimension reduction via ranking marginal quantile utilities.
  • Model averaging applied to selected covariates.
  • Delete-one cross-validation for model weight selection.
  • Theoretical analysis using empirical process theory.

Main Results:

  • The proposed estimator demonstrates optimal asymptotic properties.
  • The method is robust to the conventional assumption of weights summing to one.
  • Empirical performance surpasses LASSO and SCAD penalized regression methods.

Conclusions:

  • The developed method provides a powerful tool for high-dimensional quantile regression.
  • It offers improved accuracy and robustness compared to existing techniques.
  • The approach is validated through application to gene expression data.