Bayesian Regression with Nonparametric Heteroskedasticity

• Activity Number: 312
• Type: Invited
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Council of Chapters
• Author(s): Andriy Norets*+
• Companies: Princeton University
• Keywords: Bayesian regression ; heteroskedasticity ; misspecification ; semiparametric Bernstein - von Mises theorem ; posterior consistency ; semiparametric efficiency

Abstract

This paper presents a large sample justification for a semiparametric Bayesian approach to inference in a linear regression model. The approach is to model the distribution of the error term by a normal distribution with the variance that is a flexible function of covariates. It is shown that even when the data generating distribution of the error term is not normal the posterior distribution of the linear coefficients converges to a normal distribution with the mean equal to the asymptotically efficient estimator and the variance given by the semiparametric efficiency bound. This implies that the estimation procedure is robust and conservative from the Bayesian standpoint and at the same time it can be used as an implementation of semiparametrically efficient frequentist inference.