Addressing both variable selection and misclassified responses with parametric and semiparametric methods

While variable selection has received extensive attention in the literature, its exploration in the presence of response measurement error remains underexplored. In this paper, we investigate this important problem within the context of binary classification with error-prone responses. We present valid variable selection procedures to address the complexities of response errors. Leveraging validation data, we introduce both parametric and semiparametric methodologies to accommodate the mismeasurement effects. By rigorously establishing theoretical results, we offer insights and justifications of the validity of the proposed methods. By properly choosing {the} penalty function and regularization parameter, we demonstrate that the resulting estimators possess the oracle property. To assess the finite sample properties of the proposed methods, we conduct numerical studies that confirm the effectiveness of our proposed methods.