Variable selection in multivariate regression models with measurement error in covariates

Abstract

Multivariate regression models have been broadly used in analyzing data having multi-dimensional response variables. The use of such models is, however, impeded by the presence of measurement error and spurious variables. While data with such features are common in applications, there has been little work available concerning these features jointly. In this article, we consider variable selection under multivariate regression models with covariates subject to measurement error. To gain flexibility, we allow the dimensions of the covariate and response variables to be either fixed or diverging as the sample size increases. A new regularized method is proposed to handle both variable selection and measurement error effects for error-contaminated data. Our proposed penalized bias-corrected least squares method offers flexibility in selecting the penalty function from a class of functions with different features. Importantly, our method does not require full distributional assumptions for the associated variables, thereby broadening its applicability. We rigorously establish theoretical results and describe a computationally efficient procedure for the proposed method. Numerical studies confirm the satisfactory performance of the proposed method under finite settings, and also demonstrate deleterious effects of ignoring measurement error in inferential procedures.