Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 10, Number 2 (2016), 3045-3062.
On Bayesian robust regression with diverging number of predictors
This paper concerns the robust regression model when the number of predictors and the number of observations grow in a similar rate. Theory for M-estimators in this regime has been recently developed by several authors (El Karoui et al., 2013; Bean et al., 2013; Donoho and Montanari, 2013). Motivated by the inability of M-estimators to successfully estimate the Euclidean norm of the coefficient vector, we consider a Bayesian framework for this model. We suggest a two-component mixture of normals prior for the coefficients and develop a Gibbs sampler procedure for sampling from relevant posterior distributions, while utilizing a scale mixture of normal representation for the error distribution. Unlike M-estimators, the proposed Bayes estimator is consistent in the Euclidean norm sense. Simulation results demonstrate the superiority of the Bayes estimator over traditional estimation methods.
Electron. J. Statist., Volume 10, Number 2 (2016), 3045-3062.
Received: July 2015
First available in Project Euclid: 9 November 2016
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Nevo, Daniel; Ritov, Ya’acov. On Bayesian robust regression with diverging number of predictors. Electron. J. Statist. 10 (2016), no. 2, 3045--3062. doi:10.1214/16-EJS1205. https://projecteuclid.org/euclid.ejs/1478660516
- Supplementary materials for “On Bayesian robust regression with diverging number of predictors”.