High-dimensional Bayesian Tobit regression for censored response with Horseshoe prior
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909608704999424 |
|---|---|
| author | Mai, The Tien |
| author_facet | Mai, The Tien |
| contents | Censored response variables--where outcomes are only partially observed due to known bounds--arise in numerous scientific domains and present serious challenges for regression analysis. The Tobit model, a classical solution for handling left-censoring, has been widely used in economics and beyond. However, with the increasing prevalence of high-dimensional data, where the number of covariates exceeds the sample size, traditional Tobit methods become inadequate. While frequentist approaches for high-dimensional Tobit regression have recently been developed, notably through Lasso-based estimators, the Bayesian literature remains sparse and lacks theoretical guarantees. In this work, we propose a novel Bayesian framework for high-dimensional Tobit regression that addresses both censoring and sparsity. Our method leverages the Horseshoe prior to induce shrinkage and employs a data augmentation strategy to facilitate efficient posterior computation via Gibbs sampling. We establish posterior consistency and derive concentration rates under sparsity, providing the first theoretical results for Bayesian Tobit models in high dimensions. Numerical experiments show that our approach outperforms favorably with the recent Lasso-Tobit method.
Our method is implemented in the R package tobitbayes, which can be found on Github. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-dimensional Bayesian Tobit regression for censored response with Horseshoe prior Mai, The Tien Methodology Statistics Theory Machine Learning Censored response variables--where outcomes are only partially observed due to known bounds--arise in numerous scientific domains and present serious challenges for regression analysis. The Tobit model, a classical solution for handling left-censoring, has been widely used in economics and beyond. However, with the increasing prevalence of high-dimensional data, where the number of covariates exceeds the sample size, traditional Tobit methods become inadequate. While frequentist approaches for high-dimensional Tobit regression have recently been developed, notably through Lasso-based estimators, the Bayesian literature remains sparse and lacks theoretical guarantees. In this work, we propose a novel Bayesian framework for high-dimensional Tobit regression that addresses both censoring and sparsity. Our method leverages the Horseshoe prior to induce shrinkage and employs a data augmentation strategy to facilitate efficient posterior computation via Gibbs sampling. We establish posterior consistency and derive concentration rates under sparsity, providing the first theoretical results for Bayesian Tobit models in high dimensions. Numerical experiments show that our approach outperforms favorably with the recent Lasso-Tobit method. Our method is implemented in the R package tobitbayes, which can be found on Github. |
| title | High-dimensional Bayesian Tobit regression for censored response with Horseshoe prior |
| topic | Methodology Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2505.08288 |