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A robust and efficient change point detection method for high-dimensional linear models.

Zhong-Cheng Han1, Kong-Sheng Zhang2, Yan-Yong Zhao1

  • 1School of Statistics and Mathematics, Nanjing Audit University, Nanjing, People's Republic of China.

Journal of Applied Statistics
|July 4, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces modal linear regression for high-dimensional data, efficiently estimating differing regression coefficients across subpopulations. The method also performs variable selection and change point detection for robust analysis.

Keywords:
EM algorithmVariable selectionchange pointkick-one-offmodal

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Estimating regression coefficients is crucial in linear models.
  • Unknown coefficient parameters can vary across different segments of data.
  • High-dimensional covariates pose challenges in traditional regression analysis.

Purpose of the Study:

  • To propose a novel method for analyzing linear models with potentially different regression coefficients in two subpopulations, especially in high-dimensional settings.
  • To introduce modal linear regression for robust and efficient estimation of unknown coefficient parameters.
  • To develop a method capable of variable selection and change point detection.

Main Methods:

  • Modal linear regression is introduced for parameter estimation.
  • Variable selection and change point detection are integrated into the proposed method.
  • An estimation algorithm combining kick-one-off and SCAD approaches is developed.

Main Results:

  • The proposed modal linear regression method offers robustness and efficiency.
  • The method demonstrates capability in variable selection and change point detection.
  • The limiting behavior of the proposed method is established under mild assumptions.

Conclusions:

  • Modal linear regression provides an effective approach for high-dimensional linear models with varying coefficients.
  • The developed algorithm facilitates practical implementation and assessment via simulations and real data analysis.
  • The study contributes a versatile tool for analyzing segmented data with complex coefficient structures.