Speed of convergence in nonparametric kernel estimation of a regression function and its derivatives

zbMath0568.62042MaRDI QIDQ1060511

Alexander A. Georgiev

Publication date: 1984

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

zbMATH Keywords

uniform convergencerates of convergencestrong consistencymean square consistencynew class of kernel estimatespth order derivatives

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Nonparametric estimation (62G05) General nonlinear regression (62J02)

Related Items (8)

Consistent nonparametric multiple regression: the fixed design case ⋮ Nonparametric estimation of a regression function by delta sequences ⋮ Maximal moment inequality for partial sums of strong mixing sequences and application ⋮ Some results about kernel estimators for function derivatives based on stationary and ergodic continuous time processes with applications ⋮ Uniformly asymptotic normality of the regression weighted estimator for negatively associated samples. ⋮ Fixed design regression for time series: Asymptotic normality ⋮ Empirical likelihood based inference for the derivative of the nonparametric regression function ⋮ Asymptotics for function derivatives estimators based on stationary and ergodic discrete time processes

Cites Work

• On the Glivenko-Cantelli theorem for weighted empiricals based on independent random variables
• Consistent nonparametric regression. Discussion
• A uniform bound for the deviation of empirical distribution functions
• Contributions to the theory of nonparametric regression, with application to system identification
• Nonparametric Estimation of a Regression Function: Limiting Distribution2
• Estimation Non-paramétrique de la Régression: Revue Bibliographique
• Nonparametric estimation of a regression function
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