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Consistent Estimation of Generalized Linear Models with High Dimensional Predictors via Stepwise Regression.

Alex Pijyan1, Qi Zheng2, Hyokyoung G Hong1

  • 1Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA.

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Summary
This summary is machine-generated.

We developed a new stepwise method for building accurate predictive models using ultrahigh-dimensional data. This approach provides a final model with unbiased estimates, controlling both false negatives and false positives for better risk factor analysis.

Keywords:
estimation consistencygeneralized linear modelshigh dimensional predictorsmodel selectionstepwise regression

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Area of Science:

  • Statistics
  • Biostatistics
  • Machine Learning

Background:

  • Penalized regression methods like LASSO are common for predictive modeling but yield biased estimates.
  • Ultrahigh-dimensional data requires variable screening before penalized regression can be applied.
  • Existing methods struggle with bias and variable selection in ultrahigh-dimensional settings.

Purpose of the Study:

  • To propose a novel stepwise procedure for fitting generalized linear models with ultrahigh-dimensional predictors.
  • To develop a method that provides a final model with consistent estimates and controls for false positives and negatives.
  • To offer a reliable tool for accurately gauging the effect size of risk factors in complex datasets.

Main Methods:

  • A stepwise procedure for fitting generalized linear models.
  • Variable screening and selection integrated into a stepwise approach.
  • Development of methods for consistent estimation in ultrahigh-dimensional settings.

Main Results:

  • The proposed procedure yields a final model with consistent estimates.
  • The method effectively controls both false negatives and false positives.
  • Simulations and clinical study applications demonstrate the procedure's utility.

Conclusions:

  • The stepwise procedure offers a robust solution for predictive modeling with ultrahigh-dimensional data.
  • Consistent estimates improve the accuracy of risk factor effect size assessment.
  • This method enhances decision-making by providing reliable predictive models.