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May 2019 Bayesian robustness to outliers in linear regression and ratio estimation
Alain Desgagné, Philippe Gagnon
Braz. J. Probab. Stat. 33(2): 205-221 (May 2019). DOI: 10.1214/17-BJPS385


Whole robustness is a nice property to have for statistical models. It implies that the impact of outliers gradually vanishes as they approach plus or minus infinity. So far, the Bayesian literature provides results that ensure whole robustness for the location-scale model. In this paper, we make two contributions. First, we generalise the results to attain whole robustness in simple linear regression through the origin, which is a necessary step towards results for general linear regression models. We allow the variance of the error term to depend on the explanatory variable. This flexibility leads to the second contribution: we provide a simple Bayesian approach to robustly estimate finite population means and ratios. The strategy to attain whole robustness is simple since it lies in replacing the traditional normal assumption on the error term by a super heavy-tailed distribution assumption. As a result, users can estimate the parameters as usual, using the posterior distribution.


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Alain Desgagné. Philippe Gagnon. "Bayesian robustness to outliers in linear regression and ratio estimation." Braz. J. Probab. Stat. 33 (2) 205 - 221, May 2019.


Received: 1 December 2016; Accepted: 1 October 2017; Published: May 2019
First available in Project Euclid: 4 March 2019

zbMATH: 07057445
MathSciNet: MR3919021
Digital Object Identifier: 10.1214/17-BJPS385

Keywords: Built-in robustness , finite populations , population means , ratio estimator , simple linear regression , super heavy-tailed distributions

Rights: Copyright © 2019 Brazilian Statistical Association


Vol.33 • No. 2 • May 2019
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