Smooth estimation of a distribution and density function on a hypercube using Bernstein polynomials for dependent random vectors
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- 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.
- Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
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- 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.
- 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.
- Alexandre Leblanc, 2009. "Chung–Smirnov property for Bernstein estimators of distribution functions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(2), pages 133-142.
- Pierre Lafaye de Micheaux & Frédéric Ouimet, 2021. "A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions," Mathematics, MDPI, vol. 9(20), pages 1-35, October.
- Baker, Rose, 2008. "An order-statistics-based method for constructing multivariate distributions with fixed marginals," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2312-2327, November.
- 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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- 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.
- Janssen, Paul & Swanepoel, Jan & Veraverbeke, Noël, 2014. "A note on the asymptotic behavior of the Bernstein estimator of the copula density," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 480-487.
- 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.
- Liu, Bowen & Ghosh, Sujit K., 2020. "On empirical estimation of mode based on weakly dependent samples," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
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Keywords
Asymptotic normality Kernel estimator Non-parametric density estimation Strong consistency Strong mixing;Statistics
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