  Microarray studies, in order to identify genes associated with an outcome of
interest, usually produce noisy measurements for a large number of gene
expression features from a small number of subjects. One common approach to
analyzing such high-dimensional data is to use linear errors-in-variables
models; however, current methods for fitting such models are computationally
expensive. In this paper, we present two efficient screening procedures, namely
corrected penalized marginal screening and corrected sure independence
screening, to reduce the number of variables for final model building. Both
screening procedures are based on fitting corrected marginal regression models
relating the outcome to each contaminated covariate separately, which can be
computed efficiently even with a large number of features. Under mild
conditions, we show that these procedures achieve screening consistency and
reduce the number of features considerably, even when the number of covariates
grows exponentially with the sample size. Additionally, if the true covariates
are weakly correlated, corrected penalized marginal screening can achieve full
variable selection consistency. Through simulation studies and an analysis of
gene expression data for bone mineral density of Norwegian women, we
demonstrate that the two new screening procedures make estimation of linear
errors-in-variables models computationally scalable in high dimensional
settings, and improve finite sample estimation and selection performance
compared with estimators that do not employ a screening stage.
