On the properties of Hermite series based distribution function estimators

DOI10.1007/s00184-020-00785-zzbMath1475.62136OpenAlexW3041461031MaRDI QIDQ2036312

Michael Stephanou, Melvin M. Varughese

Publication date: 28 June 2021

Published in: Metrika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00184-020-00785-z

zbMATH Keywords

robustnessmean squared erroralmost sure convergenceinfluence functionsHermite series distribution function estimatorsequential distribution function estimators

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric robustness (62G35) Nonparametric estimation (62G05) Sequential estimation (62L12)

Related Items (1)

Sequential estimation of Spearman rank correlation using Hermite series estimators

Uses Software

• DLMF

Cites Work

• Sequential quantiles via Hermite series density estimation
• Hermite series estimates of a probability density and its derivatives
• Hermite series estimators for probability densities
• Pointwise consistency of the Hermite series density estimate
• Exact mean integrated squared error
• Properties of Hermite series estimation of probability density
• Application of Bernstein polynomials for smooth estimation of a distribution and density function
• Bandwidth selection for kernel distribution function estimation
• On estimating distribution functions using Bernstein polynomials
• The stochastic approximation method for estimation of a distribution function
• On certain integral operators associated with Hermite and Laguerre polynomials
• Polynomial and spline estimators of the distribution function with prescribed accuracy
• The Influence Curve and Its Role in Robust Estimation
• Asymptotic Statistics
• Recursive distribution estimator defined by stochastic approximation method using Bernstein polynomials
• Estimation of the quantile function using Bernstein–Durrmeyer polynomials
• Some New Estimates for Distribution Functions
• Estimation of Probability Density by an Orthogonal Series
• Bounds on Moments of Certain Random Variables
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