The Annals of Statistics
- Ann. Statist.
- Volume 31, Number 1 (2003), 174-200.
Nonparametric estimation of convex models via mixtures
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.
Ann. Statist., Volume 31, Number 1 (2003), 174-200.
First available in Project Euclid: 26 February 2003
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G07: Density estimation
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures
Hoff, Peter D. Nonparametric estimation of convex models via mixtures. Ann. Statist. 31 (2003), no. 1, 174--200. doi:10.1214/aos/1046294461. https://projecteuclid.org/euclid.aos/1046294461