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Modified check loss for efficient estimation via model selection in quantile regression.

Yoonsuh Jung1, Steven N MacEachern2, Hang Joon Kim3

  • 1Department of Statistics, Korea University, Seoul, South Korea.

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|June 16, 2022
PubMed
Summary
This summary is machine-generated.

The standard check loss for quantile regression can overfit data during validation. An L2-adjusted check loss is proposed to mitigate this overfitting by rounding its central corner, improving model reliability.

Keywords:
Check losscross-validationquantile regressionquantile regression splinequantile smoothing spline

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Area of Science:

  • Statistics
  • Machine Learning

Background:

  • The check loss function is fundamental for quantile regression and is often used for model validation when the true data distribution is unknown.
  • Empirical studies reveal that relying solely on check loss for validation can lead to overfitting, compromising model generalization.

Purpose of the Study:

  • To address the overfitting issue associated with the standard check loss function in quantile regression.
  • To introduce and evaluate a modified L2-adjusted check loss function designed to improve validation robustness.

Main Methods:

  • A novel L2-adjusted check loss function is proposed, featuring a rounded central 'corner' to smooth its behavior.
  • The adjustment mechanism is designed to diminish as the sample size increases, ensuring asymptotic consistency.
  • The performance of the modified loss function is empirically assessed through simulations involving linear and nonlinear regression models.

Main Results:

  • The L2-adjusted check loss demonstrates a reduced tendency to overfit compared to the standard check loss.
  • The modification effectively guards against overfitting, particularly in scenarios where the true distribution is unknown.
  • Simulations confirm the practical benefits of the quadratic adjustment in enhancing validation accuracy.

Conclusions:

  • The proposed L2-adjusted check loss offers a more reliable validation strategy for quantile regression, mitigating overfitting.
  • This modification provides a valuable tool for practitioners seeking to improve the generalization performance of their quantile regression models.