Weak and strong uniform consistency of a kernel error density estimator in nonparametric regression

DOI10.1016/S0378-3758(02)00417-2zbMath1031.62025MaRDI QIDQ1417796

Fuxia Cheng

Publication date: 6 January 2004

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

zbMATH Keywords

Kernel density estimationEmpirical processNonparametric residuals

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20)

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Cites Work

• The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality
• Asymptotic behavior of the empiric distribution of M-estimated residuals from a regression model with many parameters
• Strong uniform consistency rates for estimators of conditional functionals
• The empirical distribution function of residuals from generalised regression
• A weak convergence result useful in robust autoregression
• Behavior of robust estimators in the regression model with dependent errors
• Weak convergence of randomly weighted dependent residual empiricals with applications to autoregression
• Consistency of error density and distribution function estimators in nonparametric regression.
• Nonparametric statistics for stochastic processes
• Empirical process of residuals for high-dimensional linear models
• Asymptotics of some estimators and sequential residual empiricals in nonlinear time series
• Estimation of the Distribution of Noise in an Autoregression Scheme
• Asymptotic Minimax Character of the Sample Distribution Function and of the Classical Multinomial Estimator
• Foundations of Modern Probability
• Probability Inequalities for Sums of Bounded Random Variables
• Some Convergence Theorems for Ranks and Weighted Empirical Cumulatives
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