Variable selection via penalized ridge regression with error-prone variables

Abstract

Variable selection is a fundamental topic in statistical analysis and data science. Regularization methods have been widely employed to identify informative variables related to the response. However, challenges such as collinearity and measurement error often arise in real-world datasets. In this paper, we address variable selection and estimation for linear models and focus parameters. To simultaneously handle collinearity and measurement error, we propose a valid correction strategy for error-prone continuous, binary, and discrete covariates, and develop a penalized ridge regression method to perform variable selection and estimation. We establish the theoretical properties of the proposed method, including variable selection consistency and asymptotic normality. Numerical studies are conducted to evaluate its performance, and the results demonstrate that the proposed method outperforms existing approaches.