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Tests for regression coefficients in high dimensional partially linear models.

Yan Liu1,2, Sanguo Zhang1,2, Shuangge Ma3

  • 1School of Mathematical Sciences, University of Chinese Academy of Sciences.

Statistics & Probability Letters
|May 21, 2020
PubMed
Summary
This summary is machine-generated.

We developed a U-statistics test for high-dimensional partially linear models to assess regression coefficients. This new statistical method shows reliable performance in simulations, even with limited data.

Keywords:
High-dimensional analysisPartially linear modelsRegression coefficientsU-statistics

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • High-dimensional data presents challenges for traditional statistical inference.
  • Partially linear models offer flexibility in modeling complex relationships.
  • Testing regression coefficients is crucial for model interpretability and variable selection.

Purpose of the Study:

  • To introduce a novel U-statistics test for regression coefficients in high-dimensional partially linear models.
  • To extend the test to evaluate subsets of coefficients.
  • To provide theoretical guarantees and assess practical performance.

Main Methods:

  • Development of a U-statistics test tailored for high-dimensional partially linear settings.
  • Derivation of asymptotic distributions for the proposed test statistics.
  • Extension of the methodology for testing partial coefficient sets.

Main Results:

  • The proposed U-statistics test is effective for high-dimensional partially linear models.
  • Asymptotic distributions of the test statistics are rigorously established.
  • Simulation studies confirm the satisfactory finite-sample performance of the method.

Conclusions:

  • The U-statistics test provides a robust tool for analyzing high-dimensional partially linear models.
  • The method is suitable for both full and partial coefficient testing.
  • The findings support the practical applicability of the proposed statistical test.