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Interquantile Shrinkage and Variable Selection in Quantile Regression.

Liewen Jiang1, Howard D Bondell1, Huixia Judy Wang1

  • 1Department of Statistics, North Carolina State University, Raleigh, NC 27606, U.S.A.

Computational Statistics & Data Analysis
|March 22, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces novel penalization methods for quantile regression, improving model interpretability and estimation efficiency by identifying commonalities across quantiles and selecting relevant predictors.

Keywords:
Fused adaptive lassoFused adaptive sup-normOracleQuantile regressionSmoothingVariable selection

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Conditional quantile functions offer a comprehensive view of response-covariate relationships.
  • Utilizing common features across quantiles enhances estimation efficiency and model interpretability.
  • Eliminating irrelevant predictors is crucial for robust statistical modeling.

Purpose of the Study:

  • To develop novel penalization methods for quantile regression.
  • To simultaneously identify interquantile commonality and nonzero quantile coefficients.
  • To improve estimation efficiency and model interpretability in quantile regression.

Main Methods:

  • Development of two penalization methods based on a fused penalty.
  • Encouraging sparsity of quantile coefficients and interquantile slope differences.
  • Establishing oracle properties for the proposed penalization methods.

Main Results:

  • The proposed methods effectively identify interquantile commonality and nonzero coefficients.
  • Numerical investigations show simpler model structures compared to traditional methods.
  • Demonstrated higher estimation efficiency than traditional quantile regression.

Conclusions:

  • The developed penalization methods offer a more efficient and interpretable approach to quantile regression.
  • These methods facilitate the selection of relevant predictors and identification of shared patterns across quantiles.
  • The findings suggest a significant advancement over existing quantile regression techniques.