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Fully Nonparametric Regression for Bounded Data Using Dependent Bernstein Polynomials

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  • Andrés F. Barrientos
  • Alejandro Jara
  • Fernando A. Quintana

Abstract

We propose a novel class of probability models for sets of predictor-dependent probability distributions with bounded domain. The proposal extends the Dirichlet–Bernstein 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.

Suggested Citation

  • Andrés F. Barrientos & Alejandro Jara & Fernando A. Quintana, 2017. "Fully Nonparametric Regression for Bounded Data Using Dependent Bernstein Polynomials," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 806-825, April.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:518:p:806-825
    DOI: 10.1080/01621459.2016.1180987
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    References listed on IDEAS

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    1. Barrientos, Andrés F. & Canale, Antonio, 2021. "A Bayesian goodness-of-fit test for regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).

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