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

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.