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Quantile regression shrinkage and selection via the Lqsso.

Alireza Daneshvar1, Mousa Golalizadeh1

  • 1Department of Statistics, Tarbiat Modares University, Tehran, Iran.

Journal of Biopharmaceutical Statistics
|April 10, 2023
PubMed
Summary

A new quantile regression model, lqsso-QR (least quantile shrinkage and selection operator quantile regression), enhances variable selection and estimation. This method shows superiority over existing lasso-type penalties in prediction error, validated by simulations and real-world data analysis.

Keywords:
Quantile regressionconsistencylassooracle propertyshrinkage

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Area of Science:

  • Statistics
  • Machine Learning
  • Econometrics

Background:

  • Quantile regression models are increasingly sophisticated, with ongoing research into novel penalty and loss functions.
  • Existing lasso quantile regression models may overlook randomness in penalty components.
  • Adaptive lasso quantile regression models perform simultaneous estimation and variable selection.

Purpose of the Study:

  • To introduce a novel penalty for quantile regression models that accounts for randomness.
  • To develop the least quantile shrinkage and selection operator quantile regression (lqsso-QR) model.
  • To establish conditions for consistent variable selection in lasso quantile regression and demonstrate oracle properties of lqsso-QR.

Main Methods:

  • Proposing a new penalty for quantile regression, termed lqsso-QR.
  • Deriving sufficient and necessary conditions for consistent variable selection in lasso quantile regression.
  • Applying an efficient algorithm for computation, adapted from lasso quantile regression.
  • Conducting simulation studies to compare lqsso-QR with other lasso-type penalties.

Main Results:

  • The proposed lqsso-QR model demonstrates oracle properties under mild conditions.
  • Simulation studies indicate the superiority of lqsso-QR, particularly in reducing relative prediction error.
  • The method was successfully applied to the real-life rat eye dataset.

Conclusions:

  • The lqsso-QR model offers an effective approach for simultaneous estimation and variable selection in quantile regression.
  • The proposed method outperforms existing lasso-type penalties in predictive accuracy.
  • lqsso-QR provides a valuable advancement in statistical modeling for complex datasets.