Density-free convergence properties of various estimators of entropy

DOI10.1016/0167-9473(87)90065-XzbMath0632.62031OpenAlexW1963714278MaRDI QIDQ1095528

László Györfi, Edward C. van der Meulen

Publication date: 1987

Published in: Computational Statistics and Data Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-9473(87)90065-x

zbMATH Keywords

consistencyalmost sure convergenceShannon entropydifferential entropy\(L_1\)-convergencedensity-free convergence propertiesentropy estimatorshistogram-basedhistogram-based density estimator

Mathematics Subject Classification ID

Nonparametric estimation (62G05) Strong limit theorems (60F15) Measures of information, entropy (94A17) Statistical aspects of information-theoretic topics (62B10) (L^p)-limit theorems (60F25)

Related Items (20)

The Mean Relative Entropy: An Invariant Measure of Estimation Error ⋮ The use of power transformations for improved entropy estimation ⋮ Non-parametric entropy estimators based on simple linear regression ⋮ Iterated modified histograms as dynamical systems ⋮ Entropy estimation via uniformization ⋮ On the convergence of Shannon differential entropy, and its connections with density and entropy estimation ⋮ Nonparametric estimation of the entropy using a ranked set sample ⋮ A new estimator of entropy ⋮ Non-uniform spacings processes ⋮ Information estimators for weighted observations ⋮ Estimation of an entropy-based functional ⋮ Entropy invariance for autoregressive processes constructed by linear filtering ⋮ Estimation of the Entropy Functional from Dependent Samples ⋮ Information divergence estimation based on data-dependent partitions ⋮ ESTIMATION OF MULTIVARIATE SHANNON ENTROPY USING MOMENTS ⋮ Distribution Estimates Consistent in χ²-Divergence ⋮ Maximum smoothed likelihood density estimation ⋮ Optimal bandwidth selection for re-substitution entropy estimation ⋮ An entropy characterization of the inverse Gaussian distribution and related goodness-of-fit test ⋮ Silver jubilee issue

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