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Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
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Statistical Inference for High-Dimensional Generalized Linear Models with Binary Outcomes.

T Tony Cai1, Zijian Guo2, Rong Ma3

  • 1Department of Statistics and Data Science, The Wharton School, University of Pennsylvania, Philadelphia, PA 19104.

Journal of the American Statistical Association
|June 27, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a statistical framework for high-dimensional binary generalized linear models (GLMs), offering optimal confidence intervals for regression components. The method is validated using simulations and single-cell RNA-seq data analysis.

Keywords:
AdaptivityConfidence intervalHypothesis testingLink functionsOptimalityWeighting

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Area of Science:

  • Statistics
  • Computational Biology
  • Bioinformatics

Background:

  • High-dimensional data analysis presents challenges in statistical inference.
  • Generalized linear models (GLMs) are widely used for binary outcomes.
  • Existing methods may lack optimality or adaptability in high dimensions.

Purpose of the Study:

  • Develop a unified statistical inference framework for high-dimensional binary GLMs.
  • Construct optimal confidence intervals and hypothesis tests for regression components.
  • Investigate the performance and adaptivity of the proposed methods.

Main Methods:

  • A two-step weighted bias-correction method for confidence intervals and hypothesis tests.
  • Establishment of minimax lower bounds for expected interval length.
  • Theoretical analysis of confidence interval optimality and adaptivity to sparsity.

Main Results:

  • Proposed confidence intervals are rate-optimal up to a logarithmic factor.
  • Demonstrated numerical performance via simulations.
  • Analysis of single-cell RNA-seq data revealed biological insights into cellular immune responses.

Conclusions:

  • The developed framework provides efficient and adaptive inference for high-dimensional binary GLMs.
  • The methodology offers practical applications in fields like single-cell transcriptomics.
  • Introduced novel lower bound techniques applicable to broader inference problems.