Nonparametric estimation of convex models via mixtures

• 成果类型: Article
• 署名作者: Hoff, PD
• 署名单位: University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1046294461
• 发表日期: 2003
• 页码: 174-200
• 关键词: maximum-likelihood-estimation; dirichlet processes; mixing distribution; bayesian-inference; probabilities; constraints; density; Duality; SPACES

摘要

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.