Bayes prediction density and regression estimation — A semiparametric approach |
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Authors: | R. C. Tiwari S. R. Jammalamadaka S. Chib |
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Affiliation: | 1. University of North Carolina, Charlotte, USA 2. University of California, Santa Barbara, USA 3. University of Missouri, Columbia, USA
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Abstract: | This paper is concerned with the Bayes estimation of an arbitrary multivariate density,f(x), x ? R k. Such anf(x) may be represented as a mixture of a given parametric family of densities {h (x¦θ)} with support inR k, whereθ (inR d) is chosen according to a mixing distributionG. We consider the semiparametric Bayes approach in whichG, in turn, is chosen according to a Dirichlet process prior with given parameterα. We then specialize these results whenf is expressed as a mixture of multivariate normal densitiesΦ (x¦Μ, λ) whereΜ is the mean vector and λ is the precision matrix. The results are finally applied to estimating a regression parameter. |
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