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Shape restriction of the multi-dimensional Bernstein prior for density functions

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  • Zheng, Yanbing

Abstract

Random Bernstein polynomials induces a probability measure on the space of multivariate density functions on a unit cube. For density estimation, it is important that the Bernstein prior can be restricted to an admissible class of densities with certain geometric properties of the target density. In this article, we study the shape properties such as monotonicity, convexity, and symmetry of the Bernstein prior.

Suggested Citation

  • Zheng, Yanbing, 2011. "Shape restriction of the multi-dimensional Bernstein prior for density functions," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 647-651, June.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:6:p:647-651
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    References listed on IDEAS

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    1. Yanbing Zheng & Jun Zhu & Anindya Roy, 2010. "Nonparametric Bayesian inference for the spectral density function of a random field," Biometrika, Biometrika Trust, vol. 97(1), pages 238-245.
    2. Sonia Petrone, 1999. "Random Bernstein Polynomials," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 373-393, September.
    3. I‐Shou Chang & Chao A. Hsiung & Yuh‐Jenn Wu & Che‐Chi Yang, 2005. "Bayesian Survival Analysis Using Bernstein Polynomials," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 447-466, September.
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    Cited by:

    1. Burda, Martin & Prokhorov, Artem, 2014. "Copula based factorization in Bayesian multivariate infinite mixture models," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 200-213.
    2. Xiang Zhang & Yanbing Zheng, 2014. "Nonparametric Bayesian inference for multivariate density functions using Feller priors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 321-340, June.

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