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

Tokdar, Surya T.

Sankhyā 68, No. 1, 90-110 (2006).

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.

MSC:

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

Keywords:

Dirichlet process; density estimation; regression