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Robust estimation for partially linear models with large-dimensional covariates.

LiPing Zhu1, RunZe Li2, HengJian Cui3

  • 1School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China ; The Key Laboratory of Mathematical Economics (SUFE), Ministry of Education, Shanghai 200433, China.

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Summary
This summary is machine-generated.

This study introduces robust estimation for partially linear models with many variables. It uses non-concave regularization for better covariate selection and achieves accurate parameter estimation for both linear and nonlinear parts.

Keywords:
partially linear modelsrobust model selectionsemiparametric modelssmoothly clipped absolute deviation (SCAD)

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Partially linear models are widely used in various fields.
  • Estimating parameters in high-dimensional settings presents significant challenges.
  • Robust estimation is crucial for handling outliers and improving model stability.

Purpose of the Study:

  • To develop robust estimation procedures for partially linear models with large-dimensional covariates.
  • To enhance model interpretability through non-concave regularization for covariate selection.
  • To establish theoretical guarantees for the proposed estimation methods.

Main Methods:

  • Implementing a non-concave regularization method within a robust estimation framework.
  • Utilizing robust local linear regression for nonparametric component estimation.
  • Establishing asymptotic consistency for both linear and nonlinear components.

Main Results:

  • The proposed robust estimation procedure consistently estimates parameters in partially linear models.
  • The method effectively selects important covariates in the linear component.
  • The estimates for both linear and nonlinear components achieve oracle efficiency under certain conditions.

Conclusions:

  • The developed robust estimation technique provides a reliable approach for analyzing partially linear models with high-dimensional data.
  • The non-concave regularization enhances covariate selection and model interpretability.
  • The theoretical results are supported by simulation studies and a practical application.