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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.

MSC:

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