On the asymptotic normality of \(L_ p\)-norms of empirical functionals

zbMath0831.62019MaRDI QIDQ1900830

David M. Mason, Jan Beirlant

Publication date: 24 October 1995

Published in: Mathematical Methods of Statistics (Search for Journal in Brave)

zbMATH Keywords

asymptotic normalitykernel estimatorsempirical processregression function estimationPoisson representationFourier inversiondensity estimatorshistogram estimatorsLp-normsconditional characteristic functionsempirical functionals

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Order statistics; empirical distribution functions (62G30)

Related Items (17)

Asymptotic normality of plug-in level set estimates ⋮ The \(L_1\)-norm density estimator process ⋮ On a weighted bootstrap approximation of the \(L_p\) norms of kernel density estimators ⋮ Nonparametric Independence Tests: Space Partitioning and Kernel Approaches ⋮ Asymptotics of the \(L_p\)-norms of density estimators in the first-order autoregressive models. ⋮ Uniform bounds for norms of sums of independent random functions ⋮ Asymptotic properties of plug-in level set estimators for right censored data ⋮ Nonparametric estimation and inference about the overlap of two distributions ⋮ Testing functional inequalities ⋮ Asymptotic normality of two symmetry test statistics based on the \(L_1\)-error ⋮ The law of the iterated logarithm for the integrated squared deviation of a kernel density estimator ⋮ Asymptotics for theL^p-deviation of the variance estimator under diffusion ⋮ How to get central limit theorems for global errors of estimates. ⋮ Unnamed Item ⋮ Asymptotics of the \(L_p\)-norms of density estimators in the first-order autoregressive models. ⋮ On the asymptotic normality of the \(L_2\)-error in partitioning regression estimation ⋮ On the rate of convergence of error estimates for the partitioning classification rule

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