Sankhya: The Indian Journal of Statistics

2006, Volume 68, Pt. 1, 90--110


Consistency of Dirichlet Location-scale Mixture of Normals in Density Estimation and Regression

Surya T. Tokdar, Purdue University, USA

SUMMARY. We provide sufficient conditions under which a Dirichlet location-scale mixture of normal prior achieves weak and strong posterior consistency at a true density. Our conditions involve both the prior and the true density from which observations are obtained. We consider it to be a significant improvement over the 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.

AMS (1991) subject classification. Primary 62G07, 62G08, 62G20.

Key words and phrases. Posterior consistency, Dirichlet process, location-scale mixtures, density estimation, regression.

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