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POSTERIOR CONSISTENCY IN CONDITIONAL DENSITY ESTIMATION BY COVARIATE DEPENDENT MIXTURES

Published online by Cambridge University Press:  18 November 2013

Andriy Norets  and
Justinas Pelenis
Andriy Norets*
Affiliation:
University of Illinois at Urbana-Champaign
Justinas Pelenis
Affiliation:
Institute for Advanced Studies, Vienna
*
*Address corresponding to Andriy Norets, Department of Economics, University of Illinois, 1407 W. Gregory Drive, Urbana, IL 61801; e-mail: [email protected].
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Abstract

This paper considers Bayesian nonparametric estimation of conditional densities by countable mixtures of location-scale densities with covariate dependent mixing probabilities. The mixing probabilities are modeled in two ways. First, we consider finite covariate dependent mixture models, in which the mixing probabilities are proportional to a product of a constant and a kernel and a prior on the number of mixture components is specified. Second, we consider kernel stick-breaking processes for modeling the mixing probabilities. We show that the posterior in these two models is weakly and strongly consistent for a large class of data-generating processes. A simulation study conducted in the paper demonstrates that the models can perform well in small samples.

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 3 , June 2014 , pp. 606 - 646
Copyright
Copyright © Cambridge University Press 2013 

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