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Februrary 2003 Nonparametric estimation of convex models via mixtures
Peter D. Hoff
Ann. Statist. 31(1): 174-200 (Februrary 2003). DOI: 10.1214/aos/1046294461


We present a general approach to estimating probability measures constrained to lie in a convex set. We represent constrained measures as mixtures of simple, known extreme measures, and so the problem of estimating a constrained measure becomes one of estimating an unconstrained mixing measure. Convex constraints arise in many modeling situations, such as estimation of the mean and estimation under stochastic ordering constraints. We describe mixture representation techniques for these and other situations, and discuss applications to maximum likelihood and Bayesian estimation.


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Peter D. Hoff. "Nonparametric estimation of convex models via mixtures." Ann. Statist. 31 (1) 174 - 200, Februrary 2003.


Published: Februrary 2003
First available in Project Euclid: 26 February 2003

zbMATH: 1018.62023
MathSciNet: MR1962503
Digital Object Identifier: 10.1214/aos/1046294461

Primary: 62G07
Secondary: 62C10

Keywords: Bayesian inference , Choquet's theorem , convex constraints , nonparametric estimation , stochastic ordering

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 1 • Februrary 2003
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