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Testing generalized linear models with high-dimensional nuisance parameter.

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This study introduces a computationally efficient statistical test for high-dimensional generalized linear models, crucial for analyzing gene interactions. The new method avoids computationally intensive bootstrapping, offering accurate results and robust performance in genetic association studies.

Keywords:
Dense parameterModel misspecificationU-statistics

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Area of Science:

  • Statistics
  • Genetics
  • Bioinformatics

Background:

  • Generalized linear models frequently encounter high-dimensional nuisance parameters in genetic studies (e.g., gene-environment interactions).
  • Testing the significance of high-dimensional coefficient sub-vectors is critical but often computationally demanding due to reliance on bootstrapping.

Purpose of the Study:

  • To develop a computationally efficient statistical test for high-dimensional coefficient sub-vectors in generalized linear models.
  • To provide a test with a closed-form limiting distribution, applicable to both sparse and dense parameter settings.
  • To evaluate the test's performance, including Type I error control and power under high-dimensional alternatives.

Main Methods:

  • Proposed a novel statistical test with a closed-form asymptotic distribution.
  • Analyzed theoretical properties including asymptotic Type I error correctness and power under high-dimensional alternatives.
  • Conducted extensive simulations to assess performance and robustness.
  • Applied the method to real-world data for testing gene-environment interactions in a Chinese famine sample.

Main Results:

  • The proposed test demonstrates asymptotically correct Type I error rates under regularity conditions.
  • The test exhibits good power under high-dimensional alternatives.
  • Simulations confirm the method's strong performance and robustness, even when sparsity assumptions are not strictly met.
  • Successful application to Chinese famine data for gene-environment interaction analysis.

Conclusions:

  • The developed test offers a computationally efficient alternative to existing methods for high-dimensional statistical testing in generalized linear models.
  • The method is suitable for analyzing complex genetic interactions, providing reliable results with reduced computational cost.
  • Its robustness and applicability to real genetic data highlight its practical value in bioinformatics and genetic epidemiology.