Improvements on strong uniform consistency of some known kernel estimates of a density and its derivatives

DOI10.1016/0167-7152(92)90007-RzbMath0686.62023OpenAlexW2091608789MaRDI QIDQ1262646

K. L. Mehra, Rohana J. Karunamuni

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1016/0167-7152(92)90007-r

zbMATH Keywords

bias reductionBernstein polynomialsfinite differencessmoothness assumptionsStrong uniform consistencykernel type estimatesrate of convergence results

Mathematics Subject Classification ID

Nonparametric estimation (62G05)

Related Items (9)

On the convergence of Newton's method when estimating higher dimensional parameters ⋮ Note on the minimum mean integrated squared error of kernel estimates of a distribution function and its derivatives ⋮ Weak and strong uniform consistency rates of kernel density estimates for randomly censored data ⋮ Some results about kernel estimators for function derivatives based on stationary and ergodic continuous time processes with applications ⋮ Deconvolving a density from contaminated dependent observations ⋮ Nonparametric estimation of a regression function and its derivatives under an ergodic hypothesis ⋮ Optimal convergence properties of kernel density estimators without differentiability conditions ⋮ Asymptotics for function derivatives estimators based on stationary and ergodic discrete time processes ⋮ A new smoothness quantification in kernel density estimation

Cites Work

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• Consistency of a certain class of empirical density functions
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• Weak and strong uniform consistency of the kernel estimate of a density and its derivatives
• On necessary and sufficient conditions for uniform strong consistency of estimators of a density and its derivatives
• Nonparametric Estimation of Derivatives of Average of $\mu $-Densities with Convergence rates and Applications
• Generalization of Bernstein's polynomials to the infinite interval
• On Non-Parametric Estimates of Density Functions and Regression Curves
• On Strong Consistency of Density Estimates
• Estimation of a Probability Density Function and Its Derivatives
• Curve Estimates
• Convergence Rates for Empirical Bayes Two-Action Problems II. Continuous Case
• On Estimation of a Probability Density Function and Mode
• Bernstein polynomials and semigroups of operators
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