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Two-dimensional Bernstein polynomial density estimators

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  • Axel Tenbusch

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Suggested Citation

  • Axel Tenbusch, 1994. "Two-dimensional Bernstein polynomial density estimators," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 41(1), pages 233-253, December.
    • Handle: RePEc:spr:metrik:v:41:y:1994:i:1:p:233-253
    DOI: 10.1007/BF01895321
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    Citations

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    Cited by:

    1. Dawei Lu & Lina Wang, 2021. "On the Rates of Asymptotic Normality for Bernstein Polynomial Estimators in a Triangular Array," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1519-1536, December.
    2. Lu, Lu, 2015. "On the uniform consistency of the Bernstein density estimator," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 52-61.
    3. Frédéric Ouimet, 2021. "General Formulas for the Central and Non-Central Moments of the Multinomial Distribution," Stats, MDPI, vol. 4(1), pages 1-10, January.
    4. 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.
    5. Bertin, Karine & Genest, Christian & Klutchnikoff, Nicolas & Ouimet, Frédéric, 2023. "Minimax properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    6. Zhao, Yanyun & Ausín Olivera, María Concepción & Wiper, Michael Peter, 2013. "Bayesian multivariate Bernstein polynomial density estimation," DES - Working Papers. Statistics and Econometrics. WS ws131211, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    8. Bouezmarni, Taoufik & Rombouts, Jeroen V.K. & Taamouti, Abderrahim, 2010. "Asymptotic properties of the Bernstein density copula estimator for [alpha]-mixing data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 1-10, January.
    9. Osman, Muhtarjan & Ghosh, Sujit K., 2012. "Nonparametric regression models for right-censored data using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 559-573.
    10. Belalia, Mohamed & Bouezmarni, Taoufik & Leblanc, Alexandre, 2017. "Smooth conditional distribution estimators using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 166-182.
    11. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    12. Alexandre Leblanc, 2010. "A bias-reduced approach to density estimation using Bernstein polynomials," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 459-475.
    13. Babu, G. Jogesh & Chaubey, Yogendra P., 2006. "Smooth estimation of a distribution and density function on a hypercube using Bernstein polynomials for dependent random vectors," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 959-969, May.
    14. Bouezmarni Taoufik & Ghouch El & Taamouti Abderrahim, 2013. "Bernstein estimator for unbounded copula densities," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 343-360, December.
    15. Lina Wang & Dawei Lu, 2023. "Application of Bernstein Polynomials on Estimating a Distribution and Density Function in a Triangular Array," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-14, June.
    16. Sancetta, Alessio, 2007. "Nonparametric estimation of distributions with given marginals via Bernstein-Kantorovich polynomials: L1 and pointwise convergence theory," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1376-1390, August.
    17. Alexandre Leblanc, 2012. "On estimating distribution functions using Bernstein polynomials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 919-943, October.
    18. Axel Tenbusch, 1997. "Nonparametric curve estimation with bernstein estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 1-30, January.
    19. Belalia, Mohamed, 2016. "On the asymptotic properties of the Bernstein estimator of the multivariate distribution function," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 249-256.

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