Uniform in bandwidth consistency of the kernel-type estimator of the Shannon's entropy

DOI10.1016/J.CRMA.2009.12.007zbMath1185.62072OpenAlexW2010326434MaRDI QIDQ961010

Salim Bouzebda, Issam Elhattab

Publication date: 29 March 2010

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2009.12.007

Mathematics Subject Classification ID

Density estimation (62G07) Statistical aspects of information-theoretic topics (62B10)

Related Items (10)

A note on the strong consistency of nonparametric estimation of Shannon entropy in length-biased sampling ⋮ Some results about kernel estimators for function derivatives based on stationary and ergodic continuous time processes with applications ⋮ Uniform in bandwidth consistency of conditional \(U\)-statistics adaptive to intrinsic dimension in presence of censored data ⋮ Uniform consistency and uniform in bandwidth consistency for nonparametric regression estimates and conditional U-statistics involving functional data ⋮ Uniform-in-bandwidth consistency for kernel-type estimators of Shannon's entropy ⋮ Functional Uniform-in-Bandwidth Moderate Deviation Principle for the Local Empirical Processes Involving Functional Data ⋮ Nonparametric confidence intervals for the integral of a function of an unknown density ⋮ New Entropy Estimator with an Application to Test of Normality ⋮ On the uniform-in-bandwidth consistency of the general conditionalU-statistics based on the copula representation ⋮ A note on the adaptive estimation of the differential entropy by wavelet methods

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• On Estimation of a Probability Density Function and Mode
• An empirical process approach to the uniform consistency of kernel-type function estimators
• Combinatorial methods in density estimation

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