Posterior consistency of Dirichlet location-scale mixture of normals in density estimation and regression. (English) Zbl 1193.62056

Summary: We provide sufficient conditions under which a Dirichlet location-scale mixture of normal priors achieves weak and strong posterior consistency at a true density. Our conditions involve both the prior and the true density from which the observations are obtained. We consider this to be a significant improvement over existing results since our conditions cover the case of fat tailed densities, like the Cauchy, with a standard choice for the base measure of the Dirichlet process. This provides a wider choice for using these popular mixture priors for nonparametric density estimation and semiparametric regression problems.


62G07 Density estimation
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference