Fully Nonparametric Regression for Bounded Data Using Dependent Bernstein Polynomials

• 成果类型: Article
• 署名作者: Barrientos, Andres F.; Jara, Alejandro; Quintana, Fernando A.
• 署名单位: Duke University; Pontificia Universidad Catolica de Chile
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1180987
• 发表日期: 2017
• 页码: 806-825
• 关键词: bayesian density-estimation; posterior consistency; dirichlet processes; convergence-rates; mixtures; inference; models; distributions; selection

摘要

We propose a novel class of probability models for sets of predictor-dependent probability distributions with bounded domain. The proposal extends the DirichletBernstein prior for single density estimation, by using dependent stick-breaking processes. A general model class and two simplified versions are discussed in detail. Appealing theoretical properties such as continuity, association structure, marginal distribution, large support, and consistency of the posterior distribution are established for all models. The behavior of the models is illustrated using simulated and real-life data. The simulated data are also used to compare the proposed methodology to existing methods. Supplementary materials for this article are available online.