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SEMIPARAMETRIC QUANTILE REGRESSION WITH HIGH-DIMENSIONAL COVARIATES.

Liping Zhu1, Mian Huang1, Runze Li2

  • 1School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, 200433, P. R. China.

Statistica Sinica
|February 7, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces a novel quantile regression method for semiparametric models, offering a consistent estimate of the index parameter vector. This approach is computationally efficient for high-dimensional data analysis.

Keywords:
Dimension reductionheteroscedasticitylinearity conditionlocal polynomial regressionquantile regressionsingle-index model

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Semiparametric regression models are widely used for their flexibility in capturing complex relationships.
  • Single-index models reduce dimensionality while retaining nonparametric flexibility.
  • Quantile regression is essential for understanding the full conditional distribution of the response variable.

Purpose of the Study:

  • To develop and analyze a quantile regression method for semiparametric single-index models.
  • To investigate the consistency of linear quantile regression estimates for the index parameter.
  • To propose an efficient estimation procedure for conditional quantile functions in high-dimensional settings.

Main Methods:

  • Utilizing simple linear quantile regression to estimate the index parameter vector.
  • Employing local polynomial regression for estimating the conditional quantile function.
  • Establishing asymptotic properties of the proposed estimators under mild conditions.

Main Results:

  • Demonstrated that simple linear quantile regression provides a consistent estimate of the index parameter vector, even with potential model misspecification.
  • Developed a computationally efficient procedure for estimating conditional quantiles using root-n consistent index estimates.
  • Showed that the proposed quantile function estimator achieves asymptotic efficiency comparable to knowing the true index vector.

Conclusions:

  • The proposed quantile regression approach is effective for semiparametric single-index models.
  • The method offers computational advantages, particularly for high-dimensional data.
  • The findings provide a valuable tool for robust statistical inference and prediction.