On the asymptotic properties of the Bernstein estimator of the multivariate distribution function

DOI10.1016/j.spl.2015.10.004zbMath1381.62093OpenAlexW2194243112MaRDI QIDQ273747

Mohamed Belalia

Publication date: 22 April 2016

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2015.10.004

zbMATH Keywords

mean squared errorasymptotic propertiesBernstein polynomialsdistribution function

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Asymptotic properties of nonparametric inference (62G20)

Related Items (14)

The stochastic convergence of Bernstein polynomial estimators in a triangular array ⋮ Smooth conditional distribution estimators using Bernstein polynomials ⋮ Nonparametric bivariate distribution estimation using Bernstein polynomials under right censoring ⋮ On the le Cam distance between Poisson and Gaussian experiments and the asymptotic properties of Szasz estimators ⋮ Testing symmetry for bivariate copulas using Bernstein polynomials ⋮ Bernstein polynomial distribution estimators and the Dvoretzky–Kiefer–Wolfowitz inequality ⋮ Application of Bernstein polynomials on estimating a distribution and density function in a triangular array ⋮ Multivariate multiple test procedures based on nonparametric copula estimation ⋮ A precise local limit theorem for the multinomial distribution and some applications ⋮ Complete monotonicity of multinomial probabilities and its application to Bernstein estimators on the simplex ⋮ Asymptotic properties of Bernstein estimators on the simplex ⋮ Asymptotic properties of Dirichlet kernel density estimators ⋮ On the rates of asymptotic normality for Bernstein polynomial estimators in a triangular array ⋮ Bernstein conditional density estimation with application to conditional distribution and regression functions

Cites Work

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• On the boundary properties of Bernstein polynomial estimators of density and distribution functions
• Two-dimensional Bernstein polynomial density estimators
• Application of Bernstein polynomials for smooth estimation of a distribution and density function
• On estimating distribution functions using Bernstein polynomials
• Smooth estimation of a distribution and density function on a hypercube using Bernstein polynomials for dependent random vectors
• A bias-reduced approach to density estimation using Bernstein polynomials
• Chung–Smirnov property for Bernstein estimators of distribution functions
• Bernstein polynomial probability density estimation

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