High-Dimensional Heteroscedastic Regression with an Application to eQTL Data Analysis

Z. John Daye, Jinbo Chen, Hongzhe Li

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

We consider the problem of high-dimensional regression under nonconstant error variances. Despite being a common phenomenon in biological applications, heteroscedasticity has, so far, been largely ignored in high-dimensional analysis of genomic data sets. We propose a new methodology that allows nonconstant error variances for high-dimensional estimation and model selection. Our method incorporates heteroscedasticity by simultaneously modeling both the mean and variance components via a novel doubly regularized approach. Extensive Monte Carlo simulations indicate that our proposed procedure can result in better estimation and variable selection than existing methods when heteroscedasticity arises from the presence of predictors explaining error variances and outliers. Further, we demonstrate the presence of heteroscedasticity in and apply our method to an expression quantitative trait loci (eQTLs) study of 112 yeast segregants. The new procedure can automatically account for heteroscedasticity in identifying the eQTLs that are associated with gene expression variations and lead to smaller prediction errors. These results demonstrate the importance of considering heteroscedasticity in eQTL data analysis.

Original languageEnglish (US)
Pages (from-to)316-326
Number of pages11
JournalBiometrics
Volume68
Issue number1
DOIs
StatePublished - Mar 1 2012

Keywords

  • Generalized least squares
  • Heteroscedasticity
  • Largepsmalln
  • Model selection
  • Sparse regression
  • Variance estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

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