Proving consistency of non-standard kernel estimators

DOI10.1007/S11203-012-9068-4zbMath1242.62028OpenAlexW2039457361MaRDI QIDQ438677

David M. Mason

Publication date: 31 July 2012

Published in: Statistical Inference for Stochastic Processes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11203-012-9068-4

zbMATH Keywords

distribution functionsuniform in bandwidth

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Density estimation (62G07) Strong limit theorems (60F15)

Related Items (12)

Uniform in bandwidth consistency of nonparametric regression based on copula representation ⋮ Nonparametric recursive method for kernel-type function estimators for spatial data ⋮ Uniform-in-bandwidth functional limit laws ⋮ On the strong approximation of bootstrapped empirical copula processes with applications ⋮ Uniform in bandwidth consistency of conditional \(U\)-statistics adaptive to intrinsic dimension in presence of censored data ⋮ General tests of conditional independence based on empirical processes indexed by functions ⋮ Uniform consistency and uniform in bandwidth consistency for nonparametric regression estimates and conditional U-statistics involving functional data ⋮ Resampling‐based confidence intervals for model‐free robust inference on optimal treatment regimes ⋮ Uniform in bandwidth consistency of kernel estimators of the density of mixed data ⋮ Uniform convergence rate of the kernel regression estimator adaptive to intrinsic dimension in presence of censored data ⋮ On the uniform-in-bandwidth consistency of the general conditionalU-statistics based on the copula representation ⋮ Uniform consistency and uniform in number of neighbors consistency for nonparametric regression estimates and conditional \(U\)-statistics involving functional data

Cites Work

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• Uniform in bandwidth consistency of kernel estimators of the tail index
• On projection pursuit regression
• Uniform in bandwidth consistency of conditional \(U\)-statistics
• Uniform consistency of automatic and location-adaptive delta-sequence estimators
• Functional laws of the iterated logarithm for the increments of empirical and quantile processes
• Sharper bounds for Gaussian and empirical processes
• General asymptotic confidence bands based on kernel-type function estimators
• Weak convergence and empirical processes. With applications to statistics
• Uniform in bandwidth consistency of kernel-type function estimators
• Approximating conditional distribution functions using dimension reduction
• Uniform asymptotics for kernel density estimators with variable bandwidths
• An empirical process approach to the uniform consistency of kernel-type function estimators

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