Full Robustness to Outliers in a Bayesian Simple Linear Regression Model

• Activity Number: 364
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Philippe Gagnon*+ and Alain Desgagné
• Companies: Université De Montréal and UQAM
• Keywords: Bayesian inference ; Robustness ; Linear regression ; Outliers ; Location-scale parameters ; Heavy-tailed istributions

Abstract

Full robustness to outliers in a Bayesian simple linear regression model is considered. It is shown that the simple linear regression model without intercept can be viewed as a location-scale model. A link is then made with the results of robustness in Desgagné (2011). It is shown that, with a minority of outliers, the parameters given the complete sample converge in distribution to those given the non-outlying observations, as the outliers tend to plus or minus infinity. Conditions of robustness are related to the tail thickness of the density of the error. A new family of density functions with special cases satisfying the robustness criteria, the DL-GEP, is proposed. Finally, an example will be discussed to illustrate the theoretical results.