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Consistent model identification of varying coefficient quantile regression with BIC tuning parameter selection.

Qi Zheng1, Limin Peng1

  • 1Department of Biostatistics and Bioinformatics, Emory University Atlanta GA, 30322, USA.

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|December 24, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces an adaptive LASSO method for quantile regression, enabling variable selection across the entire response distribution. This approach effectively identifies covariates influencing specific quantiles, offering a more comprehensive analysis than traditional methods.

Keywords:
Bayesian information criterionQuantile regressionShrinkage estimationVarying covariate effects

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Quantile regression analyzes covariate effects across the response distribution.
  • Covariate effects can vary significantly at different quantile levels.
  • Existing methods often focus on single quantiles, potentially missing partial or full effects.

Purpose of the Study:

  • To develop a flexible penalized quantile regression framework.
  • To enable variable selection across a continuum of quantiles.
  • To establish theoretical properties and practical performance of the proposed method.

Main Methods:

  • An adaptively weighted LASSO penalization strategy is proposed.
  • Coefficients are allowed to vary with the quantile index.
  • Oracle properties of the estimator are established.
  • A BIC-type uniform tuning parameter selector is investigated for consistent model selection.

Main Results:

  • The proposed method achieves oracle properties for coefficient function estimation.
  • The BIC-type selector ensures consistent model selection.
  • Numerical studies validate the theoretical findings.
  • The procedure demonstrates practical utility in variable selection.

Conclusions:

  • The adaptive LASSO approach provides a powerful tool for quantile regression.
  • It allows for nuanced understanding of covariate effects across the response distribution.
  • The method offers improved variable selection capabilities compared to single-quantile approaches.