Rates of convergence for the empirical quantization error

DOI10.1214/aop/1023481010zbMath1018.60032OpenAlexW2037570756MaRDI QIDQ1872278

Harald Luschgy, Siegfried Graf

Publication date: 6 May 2003

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1023481010

zbMATH Keywords

rate of convergenceempirical measureWasserstein distanceempirical quantization error

Mathematics Subject Classification ID

Classification and discrimination; cluster analysis (statistical aspects) (62H30) Inequalities; stochastic orderings (60E15) Strong limit theorems (60F15) Source coding (94A29)

Related Items (6)

Linear panel regressions with two-way unobserved heterogeneity ⋮ The local quantization behavior of absolutely continuous probabilities ⋮ On the mean speed of convergence of empirical and occupation measures in Wasserstein distance ⋮ Introduction to vector quantization and its applications for numerics ⋮ Distortion mismatch in the quantization of probability measures ⋮ Speeding Up MCMC by Efficient Data Subsampling

Cites Work

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• Probability inequalities for empirical processes and a law of the iterated logarithm
• Asymptotic properties of univariate sample k-means clusters
• The transportation cost from the uniform measure to the empirical measure in dimension \(\geq 3\)
• Mass transportation problems. Vol. 1: Theory. Vol. 2: Applications
• A space quantization method for numerical integration
• Asymptotics of the quantization errors for self-similar probabilities
• Foundations of quantization for probability distributions
• Probabilistic Analysis of Geometric Location Problems
• Steinhaus's geometric location problem for random samples in the plane
• A Concentration Inequality for the K-Median Problem
• Probability Inequalities for Sums of Bounded Random Variables

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