Stochastic Bernstein polynomials: uniform convergence in probability with rates

DOI10.1007/s10444-020-09770-6zbMath1436.62393OpenAlexW3006708556MaRDI QIDQ1987749

José A. Adell, Daniel Cárdenas-Morales

Publication date: 15 April 2020

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-020-09770-6

zbMATH Keywords

rates of convergenceconfidence banduniform convergence in probabilityBernstein-Durrmeyer polynomialsstochastic Bernstein polynomials

Mathematics Subject Classification ID

Nonparametric tolerance and confidence regions (62G15) Probability distributions: general theory (60E05) Stochastic approximation (62L20) Rate of convergence, degree of approximation (41A25)

Related Items (3)

Random linear operators arising from piecewise linear interpolation on the unit interval ⋮ Optimal stochastic Bernstein polynomials in Ditzian-Totik type modulus of smoothness ⋮ Stochastic quasi-interpolation with Bernstein polynomials

Cites Work

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• Random sampling scattered data with multivariate Bernstein polynomials
• Der Wert einiger Konstanten in der Theorie der Approximation mit Bernstein-Polynomen
• Transformations of Lebesgue-Stieltjes integrals
• Quantitative generalized Voronovskaja's formulae for Bernstein polynomials
• Bernstein-Durrmeyer operators
• Sampling scattered data with Bernstein polynomials: stochastic and deterministic error estimates
• Polynomial convergence order of stochastic Bernstein approximation
• Chebyshev type inequality for stochastic Bernstein polynomials
• Stochastic orders in preservation properties by Bernstein-type operators
• A First Course in Order Statistics
• Strong converse inequalities
• Strong converse inequalities

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