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Estimation and Inference for High Dimensional Generalized Linear Models: A Splitting and Smoothing Approach.

Zhe Fei1, Yi Li2

  • 1Department of Biostatistics, UCLA, Los Angeles, California, 90025.

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This study introduces a new statistical method for analyzing high-dimensional data in biomedical research. The approach provides reliable estimates and confidence intervals for disease risk prediction, aiding clinical decisions.

Keywords:
Confidence intervalsdimension reductionhigh dimensional inference for GLMssparsitysure screening

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Area of Science:

  • Biostatistics
  • Computational Biology
  • Epidemiology

Background:

  • Modern biomedical research increasingly focuses on joint effects of high-dimensional predictors on disease risks.
  • Quantifying uncertainty in these estimates is crucial for prevention and treatment decisions.
  • Existing literature lacks inference methods for high-dimensional generalized linear models.

Purpose of the Study:

  • To propose a novel and computationally feasible inference method for high-dimensional generalized linear models.
  • To accommodate various outcome types including normal, binomial, and Poisson data.
  • To provide consistent estimates and confidence intervals for predictors.

Main Methods:

  • A "splitting and smoothing" approach is utilized.
  • Samples are split for variable selection and partial regression.
  • Estimates are averaged over multiple random splits for numerical stability.

Main Results:

  • The proposed method yields smoothed, numerically stable estimates.
  • Estimates are shown to be consistent and asymptotically normal.
  • Confidence intervals with proper coverage probabilities are constructed for predictors.

Conclusions:

  • The novel method offers a reliable approach for inference in high-dimensional generalized linear models.
  • It accommodates diverse data types and provides stable, statistically sound results.
  • The method's performance is validated through simulations and a lung cancer cohort study analysis.