Desgagné, Alain; Gagnon, Philippe Bayesian robustness to outliers in linear regression and ratio estimation. (English) Zbl 1418.62270 Braz. J. Probab. Stat. 33, No. 2, 205-221 (2019). Authors’ abstract: 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. Reviewer: Alessandro Selvitella (Fort Wayne) Cited in 8 Documents MSC: 62J05 Linear regression; mixed models 62F15 Bayesian inference 62F35 Robustness and adaptive procedures (parametric inference) Keywords:built-in robustness; simple linear regression; ratio estimator; finite populations; population means; super heavy-tailed distributions × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid