Nonparametric estimation of convex models via mixtures

DOI10.1214/aos/1046294461zbMath1018.62023OpenAlexW2083100205MaRDI QIDQ1394762

Peter D. Hoff

Publication date: 14 September 2003

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1046294461

zbMATH Keywords

stochastic orderingBayesian inferenceconvex constraintsChoquet's theorem

Mathematics Subject Classification ID

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

Related Items (12)

Bayes discriminant rules with ordered predictors ⋮ Universal inference ⋮ Generalized moment theory and Bayesian robustness analysis for hierarchical mixture models ⋮ Semiparametric Bayesian inference for mean-covariance regression models ⋮ Constrained nonparametric maximum likelihood estimation of stochastically ordered survivor functions ⋮ Semiparametric Bayes hierarchical models with mean and variance constraints ⋮ Discrete mixture representations of parametric distribution families: geometry and statistics ⋮ Flexible Bayesian quantile regression for independent and clustered data ⋮ Shape restriction of the multi-dimensional Bernstein prior for density functions ⋮ Nonparametric Bayesian models for a spatial covariance ⋮ Nonparametric Bayesian modelling for item response ⋮ Semiparametric Bayesian analysis for longitudinal mixed effects models with non-normal AR(1) errors

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Empirical likelihood ratio confidence regions
• On a class of Bayesian nonparametric estimates: I. Density estimates
• Bayes methods for a symmetric unimodal density and its mode
• The geometry of mixture likelihoods: A general theory
• Bayesian nonparametric estimation of the median. I: Computation of the estimates
• On the consistency of Bayes estimates
• Consistency of maximum likelihood estimators for certain nonparametric families, in particular: Mixtures
• Conditional distributions as derivatives
• Finite exchangeable sequences
• Consistent estimation of a mixing distribution
• Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems
• Stochastic inequalities on partially ordered spaces
• Integral representation in the set solutions of a generalized moment problem
• Sufficient statistics and extreme points
• Restricted multinomial maximum likelihood estimation based upon Fenchel duality
• A note on the Dirichlet process prior in Bayesian nonparametric inference with partial exchangeability
• Ferguson distributions via Polya urn schemes
• Maximum likelihood estimates via duality for log-convex models when cell probabilities are subject to convex constraints
• Prior distributions on spaces of probability measures
• A review of reliable maximum likelihood algorithms for semiparametric mixture models
• A Bayesian analysis of some nonparametric problems
• Contributions to the theory of Dirichlet processes
• Asymptotic normality in mixture models
• Bayesian Inference for Semiparametric Binary Regression
• Empirical likelihood ratio confidence intervals for a single functional
• Nonparametric maximum likelihood estimation of survival functions with a general stochastic ordering and its dual
• An Algorithm for Computing the Nonparametric MLE of a Mixing Distribution
• The numerical evaluation of the maximum-likelihood estimate of mixture proportions
• Some iterative procedures for generating nonsingular optimal designs
• Uniqueness of estimation and identifiability in mixture models
• Bayesian Inference of Survival Probabilities, Under Stochastic Ordering Constraints
• A Unified Approach to Likelihood Inference on Stochastic Orderings in a Nonparametric Context
• Maximum Likelihood Estimation of the Distributions of Two Stochastically Ordered Random Variables
• Probability Densities with Given Marginals

This page was built for publication: Nonparametric estimation of convex models via mixtures