Weak limit theorems for univariate \(k\)-mean clustering under a nonregular condition

DOI10.1016/0047-259X(92)90070-VzbMath0753.60026MaRDI QIDQ1192003

Regis J. Serinko, Gutti Jogesh Babu

Publication date: 27 September 1992

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

rate of convergenceasymptotic normalitymaximum likelihooddouble exponential distributionnormal limiting distributionBahadur's representationsingular Hessian

Mathematics Subject Classification ID

Classification and discrimination; cluster analysis (statistical aspects) (62H30) Central limit and other weak theorems (60F05)

Related Items (8)

Asymptotics of \(k\)-mean clustering under non-i.i.d. sampling ⋮ Trimmed \(k\)-means: An attempt to robustify quantizers ⋮ Nonparametric K-means algorithm with applications in economic and functional data ⋮ Spatial point processes in astronomy ⋮ Asymptotics of a clustering criterion for smooth distributions ⋮ On the asymptotics of trimmed best \(k\)-nets ⋮ Asymptotics of the empirical cross-over function ⋮ A central limit theorem for multivariate generalized trimmed \(k\)-means

Cites Work

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• Strong consistency of k-means clustering
• A central limit theorem for k-means clustering
• Asymptotic distributions for clustering criteria
• On Grouping for Maximum Homogeneity
• Quantization and the method of<tex>k</tex>-means
• A Note on Quantiles in Large Samples

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