We consider the problem of high-dimensional regression under non-constant 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 non-constant 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.
|Evidence ID||Analyze ID||Interactor||Interactor Systematic Name||Interactor||Interactor Systematic Name||Type||Assay||Annotation||Action||Modification||Phenotype||Source||Reference||Note|
|Evidence ID||Analyze ID||Gene||Gene Systematic Name||Gene Ontology Term||Gene Ontology Term ID||Qualifier||Aspect||Method||Evidence||Source||Assigned On||Annotation Extension||Reference|
|Evidence ID||Analyze ID||Gene||Gene Systematic Name||Phenotype||Experiment Type||Experiment Type Category||Mutant Information||Strain Background||Chemical||Details||Reference|
|Evidence ID||Analyze ID||Regulator||Regulator Systematic Name||Target||Target Systematic Name||Experiment||Assay||Construct||Conditions||Strain Background||Reference|