{"ID":2890266,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.20079","arxiv_id":"2507.20079","title":"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 $\\ell_1$-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 $\\ell_1$-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.","short_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., wit...","url_abs":"https://arxiv.org/abs/2507.20079","url_pdf":"https://arxiv.org/pdf/2507.20079v1","authors":"[\"Niloofar Ramezani\",\"Martin Slawski\"]","published":"2025-07-26T23:19:17Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"math.ST\",\"stat.ML\"]","methods":"[]","has_code":false}