Screening methods for linear errors‐in‐variables models in high dimensions.

This article focuses on developing two computationally efficient screening procedures—corrected penalized marginal screening (PMSc) and corrected sure independence screening (SISc)—for high-dimensional linear errors-in-variables (EIV) models, which are commonly used in microarray studies with noisy gene expression data. Both methods fit corrected marginal regressions of the outcome on each contaminated covariate separately, enabling scalable variable screening that retains all important variables (screening consistency) even when the number of covariates grows exponentially with sample size. Theoretical results establish that PMSc can achieve full variable selection consistency under a partial orthogonality condition among true covariates, while SISc can reduce dimensionality below sample size while retaining relevant variables under certain distributional assumptions. Simulation studies and an application to bone mineral density gene expression data from Norwegian women demonstrate that these two-stage screening procedures substantially improve estimation accuracy and variable selection performance compared to one-stage estimators, while greatly reducing computational cost. The authors note that these screening methods can be integrated with various existing measurement error correction techniques and suggest future extensions to more complex models and iterative screening to address highly correlated covariates.