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Two-Sample Tests for High-Dimensional Linear Regression with an Application to Detecting Interactions.

Yin Xia1, Tianxi Cai2, T Tony Cai3

  • 1Department of Statistics, School of Management, Fudan University and Department of Statistics & Operations Research, University of North Carolina at Chapel Hill.

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Summary
This summary is machine-generated.

This study introduces novel statistical tests for comparing high-dimensional linear regression models, crucial for genomic applications. The methods effectively control error rates and identify genetic associations, even with sparse data.

Keywords:
False discovery proportionfalse discovery ratehigh-dimensional linear regressionhypothesis testingmultiple comparisonssparsitytwo-sample tests

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Area of Science:

  • Genomics
  • Statistical Genetics
  • High-Dimensional Data Analysis

Background:

  • Genomic studies often involve complex, high-dimensional datasets.
  • Comparing linear regression models is essential for identifying genetic associations.
  • Existing methods may lack power or efficiency in high-dimensional settings.

Purpose of the Study:

  • To develop and validate novel statistical testing procedures for comparing two high-dimensional linear regression models.
  • To address global and multiple testing problems in genomic data analysis.
  • To identify genetic variants associated with traits by analyzing interactions.

Main Methods:

  • Development of a global testing procedure for equality of regression vectors.
  • Introduction of a multiple testing procedure controlling false discovery rate and proportion.
  • Theoretical analysis of test validity and optimality under sparsity.
  • Simulation studies and real-data analysis using the Framingham Offspring study.

Main Results:

  • The proposed global test demonstrates high power against sparse alternatives.
  • The multiple testing procedure effectively controls error rates (false discovery rate and false discovery proportion).
  • Tests maintain desired error rates under null hypothesis and exhibit good power at moderate sample sizes.
  • Application to Framingham data revealed insights into gene-environment interactions for inflammation markers.

Conclusions:

  • The developed statistical tests are powerful, valid, and easy to implement for high-dimensional genomic data.
  • These methods enhance the ability to detect genetic associations and understand complex biological systems.
  • The procedures offer a robust framework for analyzing interactions between genetic factors and environmental exposures.