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Hoff, Peter D.

Nonparametric estimation of convex models via mixtures. (English) Zbl 1018.62023

Ann. Stat. 31, No. 1, 174-200 (2003).
Summary: 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.

Cited in 13 Documents

MSC:

62G07 Density estimation
62F30 Parametric inference under constraints
60E15 Inequalities; stochastic orderings
60A10 Probabilistic measure theory
62A01 Foundations and philosophical topics in statistics
62C10 Bayesian problems; characterization of Bayes procedures

Keywords:

Choquet’s theorem; convex constraints; stochastic ordering; Bayesian inference
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References:

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