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Simultaneous estimation and variable selection in median regression using Lasso-type penalty.

Jinfeng Xu1, Zhiliang Ying

  • 1Department of Statistics and Applied Probability, National University of Singapore, Singapore 117546, Singapore.

Annals of the Institute of Statistical Mathematics
|August 27, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a novel two-stage median regression method with a LASSO penalty for efficient variable selection. The approach adaptively selects penalty degrees, achieving optimal tuning parameters and an oracle property for robust statistical analysis.

Keywords:
Bayesian information criterionLassoLeast absolute deviationsMedian regressionPerturbationVariable selection

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Variable selection is crucial in high-dimensional regression.
  • Median regression offers robustness to outliers compared to mean regression.
  • LASSO (Least Absolute Shrinkage and Selection Operator) provides a penalized approach for variable selection.

Purpose of the Study:

  • To develop a robust and efficient method for variable selection in median regression.
  • To propose a data-driven procedure for adaptively selecting penalty parameters.
  • To demonstrate the theoretical properties and practical utility of the proposed method.

Main Methods:

  • A two-stage estimation and variable selection procedure is proposed.
  • A LASSO-type penalty is incorporated into median regression.
  • A Bayesian information criterion (BIC)-type approach is used for data-driven tuning parameter selection.
  • Standard linear programming is utilized for computational implementation.

Main Results:

  • The proposed method adaptively selects asymptotically optimal tuning parameters.
  • The resulting estimator is shown to possess the oracle property.
  • The method is computationally efficient and easy to implement.
  • A simple estimator for standard error is obtained using a random perturbation scheme.

Conclusions:

  • The combined median regression and LASSO penalty offers a powerful tool for variable selection.
  • The data-driven procedure ensures optimal parameter selection and robust performance.
  • The method is validated through simulations and a real-data example.