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An elastic-net penalized expectile regression with applications.

Q F Xu1,2, X H Ding1, C X Jiang1

  • 1School of Management, Hefei University of Technology, Hefei, People's Republic of China.

Journal of Applied Statistics
|June 16, 2022
PubMed
Summary

We developed an elastic-net penalized expectile regression (ER-EN) model for effective variable selection. The ER-EN model shows superior performance in variable selection and prediction compared to other regression methods, especially for asymmetric data.

Keywords:
62J05Expectile regressionSNCDelastic-nethigh-dimensional datavariable selection

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Area of Science:

  • Statistics
  • Machine Learning
  • Biostatistics

Background:

  • Variable selection is crucial in high-dimensional regression.
  • Expectile regression offers an alternative to mean and quantile regression.
  • Existing methods may lack robustness or efficiency in variable selection.

Purpose of the Study:

  • To introduce an elastic-net penalized expectile regression (ER-EN) model.
  • To develop an efficient algorithm for solving the ER-EN model in high dimensions.
  • To evaluate the performance of ER-EN against other penalized regression techniques.

Main Methods:

  • Introducing the elastic-net penalty into expectile regression.
  • Employing the semismooth Newton coordinate descent (SNCD) algorithm for model fitting.
  • Conducting extensive Monte Carlo simulations for performance evaluation.

Main Results:

  • The ER-EN model demonstrated superior variable selection and predictive accuracy.
  • ER-EN outperformed elastic-net penalized least squares (LSR-EN), Huber (HR-EN), and quantile regression (QR-EN).
  • The model showed particular effectiveness for asymmetric data distributions.

Conclusions:

  • The proposed ER-EN model is a powerful tool for variable selection in expectile regression.
  • The SNCD algorithm provides an efficient solution for high-dimensional ER-EN.
  • ER-EN offers advantages over existing methods in both simulation studies and real-world applications.