Robust Bayesian Model Averaging for Linear Regression Models With Heavy-Tailed Errors

Shamriddha De; Joyee Ghosh

doi:10.48550/arxiv.2407.16366

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Robust Bayesian Model Averaging for Linear Regression Models With Heavy-Tailed Errors

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Robust Bayesian Model Averaging for Linear Regression Models With Heavy-Tailed Errors

Shamriddha De and Joyee Ghosh

arXiv.org

Cornell University

07/23/2024

DOI: 10.48550/arxiv.2407.16366

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

In this article, our goal is to develop a method for Bayesian model averaging in linear regression models to accommodate heavier tailed error distributions than the normal distribution. Motivated by the use of the Huber loss function in presence of outliers, Park and Casella (2008) proposed the concept of the Bayesian Huberized lasso, which has been recently developed and implemented by Kawakami and Hashimoto (2023), with hyperbolic errors. Because the Huberized lasso cannot enforce regression coefficients to be exactly zero, we propose a fully Bayesian variable selection approach with spike and slab priors, that can address sparsity more effectively. Furthermore, while the hyperbolic distribution has heavier tails than a normal distribution, its tails are less heavy in comparison to a Cauchy distribution.Thus, we propose a regression model, with an error distribution that encompasses both hyperbolic and Student-t distributions. Our model aims to capture the benefit of using Huber loss, but it can also adapt to heavier tails, and unknown levels of sparsity, as necessitated by the data. We develop an efficient Gibbs sampler with Metropolis Hastings steps for posterior computation. Through simulation studies, and analyses of the benchmark Boston housing dataset and NBA player salaries in the 2022-2023 season, we show that our method is competitive with various state-of-the-art methods.

Statistics - Computation

Statistics - Methodology

Details

Title: Subtitle: Robust Bayesian Model Averaging for Linear Regression Models With Heavy-Tailed Errors
Creators: Shamriddha De
Joyee Ghosh
Resource Type: Preprint
Publication Details: arXiv.org
Publisher: Cornell University; Ithaca, New York
DOI: 10.48550/arxiv.2407.16366
eISSN: 2331-8422
Language: English
Date posted: 07/23/2024
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9984687783602771

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