Bayesian regression with nonparametric heteroskedasticity

This paper studies large sample properties of a semiparametric Bayesian approach to inference in a linear regression model. The approach is to model the distribution of the regression error term by a normal distribution with the variance that is a flexible function of covariates. The main result of the paper is a semiparametric Bernstein–von Mises theorem under misspecification: even when the distribution of the regression error term is not normal, the posterior distribution of the properly recentered and rescaled regression coefficients converges to a normal distribution with the zero mean and the variance equal to the semiparametric efficiency bound.