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Adaptive group bridge estimation for high-dimensional partially linear models.

Xiuli Wang1, Mingqiu Wang1

  • 1School of Statistics, Qufu Normal University, Jingxuan West Road, Qufu, 273165 P.R. China.

Journal of Inequalities and Applications
|July 21, 2017
PubMed
Summary
This summary is machine-generated.

We developed an adaptive group bridge method for statistical group selection in partially linear models. This approach demonstrates reliable performance for high-dimensional data analysis.

Keywords:
adaptive group bridgehigh dimensionpartially linear model

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Group selection is crucial for high-dimensional data analysis.
  • Partially linear models offer flexibility in statistical modeling.
  • Existing methods may face challenges with diverging parameter numbers.

Purpose of the Study:

  • To introduce an adaptive group bridge method for group selection.
  • To analyze the statistical properties of the proposed estimator.
  • To evaluate the method's practical utility through simulations and real-world data.

Main Methods:

  • Developing an adaptive group bridge penalty.
  • Theoretical analysis of consistency, convergence rates, and asymptotic distribution.
  • Empirical evaluation using simulation studies and a real data example.

Main Results:

  • The proposed adaptive group bridge estimator is consistent.
  • Established convergence rates and asymptotic distribution under regularity conditions.
  • Simulation results confirm the method's effectiveness in finite samples.

Conclusions:

  • The adaptive group bridge method provides a robust approach for group selection in partially linear models.
  • The theoretical properties ensure reliable estimation even with a diverging number of parameters.
  • The method shows practical applicability and good finite sample performance.