The New England Journal of Statistics in Data Science

This study explores the application of the t-link model in high-dimensional variable selection for binary regression. The t-link model provides flexibility in binary modeling and offers robust inference in the presence of outliers, making it a preferable alternative to the commonly used probit and logit links. To address the computational challenges posed by a large number of covariates, the skinny Gibbs algorithm is employed, and the consistency of variable selection under this approximate algorithm is established. These advancements in both computational and theoretical perspectives enhance the practicality and ease of implementing the t-link model. The performance of the t-link model, with a specified degrees of freedom, is compared to logit link and the probit link through simulation studies and an application to PCR data. The results demonstrate the robustness and computational efficiency of the proposed method.