The stochastic convergence of Bernstein polynomial estimators in a triangular array

DOI10.1080/10485252.2022.2107643OpenAlexW4295152298MaRDI QIDQ5051337

Publication date: 23 November 2022

Published in: Journal of Nonparametric Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10485252.2022.2107643

zbMATH Keywords

empirical process covering number triangular array Bernstein estimator stochastic equicontinuity

Mathematics Subject Classification ID

Gaussian processes (60G15) Nonparametric estimation (62G05) Probability distributions: general theory (60E05) Nonparametric inference (62Gxx)

Cites Work

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On the asymptotic properties of the Bernstein estimator of the multivariate distribution function
On the boundary properties of Bernstein polynomial estimators of density and distribution functions
The Glivenko-Cantelli problem, ten years later
Strong laws for density estimators of Bernstein type
Some limit theorems for empirical processes (with discussion)
Asymptotic distributions of smoothed histograms
Central limit theorems for empirical measures
Two-dimensional Bernstein polynomial density estimators
Application of Bernstein polynomials for smooth estimation of a distribution and density function
Weak convergence and empirical processes. With applications to statistics
On estimating distribution functions using Bernstein polynomials
Recursive density estimators based on Robbins-Monro's scheme and using Bernstein polynomials
Asymptotic properties of Bernstein estimators on the simplex
On the rates of asymptotic normality for Bernstein polynomial estimators in a triangular array
Introduction to empirical processes and semiparametric inference
Smooth estimation of a distribution and density function on a hypercube using Bernstein polynomials for dependent random vectors
Weak convergence of probabilities on nonseparable metric spaces and empirical measures on Euclidean spaces
On the rates of asymptotic normality for Bernstein density estimators in a triangular array
Remarks on Some Nonparametric Estimates of a Density Function
Approximation Theorems of Mathematical Statistics
A bias-reduced approach to density estimation using Bernstein polynomials
Chung–Smirnov property for Bernstein estimators of distribution functions
Recursive distribution estimator defined by stochastic approximation method using Bernstein polynomials
On improving convergence rate of Bernstein polynomial density estimator
On Estimation of a Probability Density Function and Mode
Heuristic Approach to the Kolmogorov-Smirnov Theorems
Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems
Convergence of stochastic processes

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