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This study introduces a novel lasso estimator for high-dimensional regression models with potential change points. The method efficiently selects variables and models, offering accurate estimation for both coefficients and threshold parameters.

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • High-dimensional regression models are increasingly used.
  • Identifying change points in data is crucial for accurate modeling.
  • Existing methods may struggle with simultaneous variable and model selection.

Purpose of the Study:

  • To develop a lasso estimator for high-dimensional regression with covariate threshold change points.
  • To enable simultaneous selection of covariates and regression models (linear vs. threshold).
  • To derive non-asymptotic oracle inequalities for prediction risk and coefficient estimation.

Main Methods:

  • Development of a unified lasso estimator for regression coefficients and threshold parameter.
  • Derivation of non-asymptotic oracle inequalities under sparsity assumptions.
  • Analysis of estimation error bounds for the threshold parameter, even in high dimensions.

Main Results:

  • The proposed lasso estimator performs simultaneous variable and model selection.
  • Oracle inequalities are established without pretesting for threshold effects.
  • Near n-1 bounds for threshold parameter estimation error are achieved, even when regressors >> sample size.

Conclusions:

  • The developed lasso method offers a robust approach for high-dimensional regression with threshold change points.
  • The method demonstrates strong theoretical guarantees and practical utility through simulations and real-data application.