Lasso Penalization for High‐Dimensional Beta Regression Models: Computation, Analysis, and Inference

ABSTRACT Beta regression is commonly employed when the outcome variable is a proportion. Since its conception, the approach has been widely used in applications spanning various scientific fields. A series of extensions have been proposed over time, several of which address variable selection and penalized estimation, e.g., with an ‐penalty (LASSO). However, a theoretical analysis of this popular approach in the context of Beta regression with high‐dimensional predictors is lacking. In this paper, we aim to close this gap. A particular challenge arises from the non‐convexity of the associated negative log‐likelihood, which we address by resorting to a framework for analyzing stationary points in a neighborhood of the target parameter. Leveraging this framework, we derive a non‐asymptotic bound on the ‐error of such stationary points. In addition, we propose a debiasing approach to construct confidence intervals for the regression parameters. A proximal gradient algorithm is devised for optimizing the resulting penalized negative log‐likelihood function. Our theoretical analysis is corroborated via simulation studies, and a real data example concerning the prediction of county‐level proportions of incarceration is presented to showcase the practical utility of our methodology.