Distribution Estimates Consistent in χ2-Divergence

DOI10.1080/02331889808802651zbMath0951.62029OpenAlexW2081376492MaRDI QIDQ4228059

Igor Vajda, László Györfi, Friedrich Liese, Edward C. van der Meulen

Publication date: 3 January 2001

Published in: Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331889808802651

zbMATH Keywords

distribution estimatorrate of consistencyBarron density estimatorconsistency in chi-square-divergence

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20)

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Cites Work

• Unnamed Item
• No empirical probability measure can converge in the total variation sense for all distributions
• Density-free convergence properties of various estimators of entropy
• Density estimation by wavelet thresholding
• Formulae for mean integrated squared error of nonlinear wavelet-based density estimators
• On some global measures of the deviations of density function estimates
• On the f-divergence and singularity of probability measures
• On arbitrarily slow rates of global convergence in density estimation
• Distribution estimation consistent in total variation and in two types of information divergence
• On the asymptotic normality of the L₁‐ and L₂‐errors in histogram density estimation
• Asymptotic Normality ofL₁-Error in Density Estimation
• Asymptotically Optimal Tests for Multinomial Distributions