Bernstein polynomial probability density estimation

DOI10.1080/1048525042000191486zbMath1080.62019OpenAlexW1986619683MaRDI QIDQ4820843

Yoshihide Kakizawa

Publication date: 1 October 2004

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

Full work available at URL: https://doi.org/10.1080/1048525042000191486

zbMATH Keywords

boundary biasmean integrated squared errorkernel estimateMSIE

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20)

Related Items (27)

Recursive regression estimation based on the two-time-scale stochastic approximation method and Bernstein polynomials ⋮ On the asymptotic properties of the Bernstein estimator of the multivariate distribution function ⋮ Unimodal density estimation using Bernstein polynomials ⋮ Bernstein polynomial of recursive regression estimation with censored data ⋮ On estimating distribution functions using Bernstein polynomials ⋮ An alternative distribution function estimation method using rational Bernstein polynomials ⋮ On the uniform consistency of the Bernstein density estimator ⋮ Application of Bernstein polynomials on estimating a distribution and density function in a triangular array ⋮ A Bernstein-type estimator for decreasing density with application to \(p\)-value adjustments ⋮ On the boundary properties of Bernstein polynomial estimators of density and distribution functions ⋮ Unnamed Item ⋮ Re-formulation of inverse Gaussian, reciprocal inverse Gaussian, and Birnbaum-Saunders kernel estimators ⋮ Generalized kernel regression estimator for dependent size-biased data ⋮ Relative density estimation for left truncated and right censored data ⋮ A bias-reduced approach to density estimation using Bernstein polynomials ⋮ Empirical relevance of ambiguity in first-price auctions ⋮ On improving convergence rate of Bernstein polynomial density estimator ⋮ A note on generalized Bernstein polynomial density estimators ⋮ Chung–Smirnov property for Bernstein estimators of distribution functions ⋮ Efficient and robust density estimation using Bernstein type polynomials ⋮ Asymptotic properties of Bernstein estimators on the simplex ⋮ Plug-in bandwidth selector for the kernel relative density estimator ⋮ Asymptotic properties of Dirichlet kernel density estimators ⋮ Bernstein conditional density estimation with application to conditional distribution and regression functions ⋮ Asymptotic properties of the Bernstein density copula estimator for \(\alpha \)-mixing data ⋮ Bernstein polynomial estimation of a spectral density ⋮ Flexible pair-copula estimation in D-vines using bivariate penalized splines

Cites Work

• Beta kernel estimators for density functions
• Asymptotic distributions of smoothed histograms
• Smoothing histograms by means of lattice- and continuous distributions
• Application of Bernstein polynomials for smooth estimation of a distribution and density function
• Convergence rates for density estimation with Bernstein polynomials.
• Remarks on Some Nonparametric Estimates of a Density Function
• Smooth optimum kernel estimators near endpoints
• Empirical likelihood confidence intervals for nonparametric density estimation
• Curve Estimates
• On Estimation of a Probability Density Function and Mode
• Unnamed Item

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