Electronic Journal of Statistics

On Bayesian robust regression with diverging number of predictors

Daniel Nevo and Ya’acov Ritov

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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.

Article information

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J05: Linear regression 62H12: Estimation 62F15: Bayesian inference

Robust regression high dimensional regression Bayesian estimation MCMC


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

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