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VARIABLE SELECTION AND ESTIMATION IN HIGH-DIMENSIONAL VARYING-COEFFICIENT MODELS.

Fengrong Wei1, Jian Huang1, Hongzhe Li1

  • 1Department of Mathematics, University of West Georgia, 1601 Maple Street, Carrollton, GA 30118, USA. fwei@westga.edu.

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Summary
This summary is machine-generated.

This study introduces the adaptive group Lasso for nonparametric varying coefficient models in high-dimensional settings. It effectively selects important variables, outperforming the standard group Lasso in sparse data scenarios.

Keywords:
Basis expansiongroup Lassohigh-dimensional datanon-parametric coefficient functionselection consistencysparsity

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Area of Science:

  • Statistics
  • Machine Learning

Background:

  • Nonparametric varying coefficient models analyze time-dependent variable effects.
  • Existing methods are limited to low-dimensional settings where variables are fewer than sample size.

Purpose of the Study:

  • To develop and evaluate variable selection and estimation methods for nonparametric varying coefficient models in sparse, high-dimensional settings.
  • To address limitations of existing methods when the number of variables exceeds the sample size.

Main Methods:

  • Application of group Lasso and basis function expansion for simultaneous variable selection and estimation.
  • Introduction and analysis of the adaptive group Lasso to improve selection accuracy.

Main Results:

  • Group Lasso achieves correct dimensionality and estimation consistency but lacks selection consistency.
  • Adaptive group Lasso demonstrates the oracle selection property, correctly identifying important variables with high probability.

Conclusions:

  • Adaptive group Lasso offers superior variable selection performance compared to group Lasso in high-dimensional varying coefficient models.
  • The proposed methods are validated through simulations and a real-world data example.