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Debiased lasso after sample splitting for estimation and inference in high-dimensional generalized linear models.

Omar Vazquez1, Bin Nan2

  • 1Department of Biostatistics, Epidemiology and Informatics, University of Pennsylvania, Philadelphia, Pennsylvania, U.S.A.

The Canadian Journal of Statistics = Revue Canadienne De Statistique
|June 4, 2025
PubMed
Summary

This study introduces a debiased lasso method with random sample splitting for high-dimensional generalized linear models. The approach improves estimation accuracy by reducing bias and variance, outperforming existing methods.

Keywords:
Asymptotic normalityPrimary 62J12Secondary 62F12genetic markerhigh dimensional inferencesingle nucleotide polymorphism (SNP)sparse regression

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Area of Science:

  • Statistics
  • Machine Learning
  • Biostatistics

Background:

  • High-dimensional generalized linear models (GLMs) present challenges in estimation and inference.
  • Variable selection and model fitting in high dimensions often suffer from bias and variance issues.

Purpose of the Study:

  • To develop and evaluate a robust method for estimation and inference in high-dimensional GLMs using random sample splitting.
  • To improve the accuracy and efficiency of statistical modeling in complex datasets.

Main Methods:

  • Employed random sample splitting to partition data into training and testing subsamples.
  • Utilized the LASSO (Least Absolute Shrinkage and Selection Operator) for initial submodel selection.
  • Applied a debiased LASSO for fitting the selected model on the remaining subsample.
  • Investigated the asymptotic normality of estimates and the impact of multiple splitting for efficiency.

Main Results:

  • The proposed sample splitting procedure with debiased LASSO yields asymptotically normal estimates.
  • Multiple splitting effectively addresses the loss of efficiency inherent in single splitting.
  • Debiased LASSO significantly reduces bias and variance compared to standard maximum likelihood methods.
  • The multiple splitting debiased LASSO method demonstrates superior numerical performance over existing approaches.

Conclusions:

  • Random sample splitting combined with debiased LASSO offers a powerful tool for high-dimensional GLMs.
  • The method provides more reliable and efficient estimates in high-dimensional settings.
  • The approach was successfully illustrated using real-world smoking data analysis.