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Robust and sparse learning of varying coefficient models with high-dimensional features.

Wei Xiong1, Maozai Tian2, Manlai Tang3

  • 1School of Statistics, University of International Business and Economics, Beijing, People's Republic of China.

Journal of Applied Statistics
|November 16, 2023
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Summary

This study introduces a novel varying coefficient model (VCM) approach using quantile-adaptive weights. It improves efficiency and prediction for complex data, outperforming traditional methods.

Keywords:
Model averagingquantile varying coefficient modelquantile-adaptive weightsvariable selection

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Area of Science:

  • Statistics
  • Data Science
  • Scientific Modeling

Background:

  • Varying coefficient models (VCMs) are crucial for analyzing dynamic predictor structures in science.
  • Classical regression struggles with skewed, heterogeneous, or heavy-tailed data.
  • Existing methods may lack efficiency in sparse or extreme-value scenarios.

Purpose of the Study:

  • To develop a robust and efficient method for varying coefficient models (VCMs).
  • To enhance least square (LS) and quantile regression (QR) using quantile-adaptive weights.
  • To improve prediction and uncover patterns in high-dimensional data.

Main Methods:

  • Incorporating model averaging with quantile-adaptive weights.
  • Developing robust procedures for VCMs, leveraging data heterogeneity and sparsity.
  • Utilizing a new iterative algorithm for consistent estimation and optimal convergence rates.

Main Results:

  • The proposed method demonstrates improved efficiency and adaptability, especially for extreme events and high-dimensional data.
  • The iterative algorithm is proven to be asymptotically consistent.
  • Simulations and real-data analyses show superior predictive power over LS, CQR, and QR.

Conclusions:

  • The novel VCM approach with quantile-adaptive weights offers a powerful tool for complex data analysis.
  • The methods effectively reveal dynamic structures and identify significant predictors in high-dimensional settings.
  • This work advances statistical modeling for scientific discovery.