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Automatic Structure Discovery for Varying-coefficient Partially Linear Models.

Guangren Yang1, Yanqing Sun2, Xia Cui3

  • 1Department of Statistics, School of Economics, Jinan University, Guangzhou, P.R. China. tygr@jnu.edu.cn.

Communications in Statistics: Theory and Methods
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Summary
This summary is machine-generated.

This study introduces a new penalized regression method to identify linear versus nonlinear covariate effects in varying-coefficient partially linear models. The approach accurately distinguishes covariate effects, enhancing model structure selection.

Keywords:
62G0862G2062J05B-splinecoordinate descent algorithmgroup MCPvarying-coefficient partially linear models

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Varying-coefficient partially linear models are crucial for analyzing covariate effects in regression.
  • A key challenge is determining which covariates exhibit linear versus nonlinear effects.

Purpose of the Study:

  • To propose a novel profile method for identifying linear and nonlinear covariate effects.
  • To enhance the model structure selection in varying-coefficient partially linear models.

Main Methods:

  • A penalized regression approach utilizing a group minimax concave penalty.
  • Development of a profile method for covariate effect identification.

Main Results:

  • The proposed method accurately distinguishes between linear and nonlinear covariate effects with high probability.
  • Theoretical results establish the convergence rate of the linear estimator and its asymptotic normality.
  • Simulation studies validate the effectiveness of the proposed method.

Conclusions:

  • The profile method offers a robust solution for model structure selection in varying-coefficient partially linear models.
  • The findings provide theoretical guarantees and empirical support for the proposed penalized regression technique.