Optimal clustering on the real line
type: Item
instance of: scholarly article
title: Optimal clustering on the real line
zbMATH Open document ID: 0666.62059
DOI: 10.1016/0047-259X(88)90104-2
author: R. W. Butler
published in: Journal of Multivariate Analysis
publication date: 1988-01-01T00:00:00Z
review text: A method is proposed for assessing the number of groups (clusters) in a random sample (presented by order statistics) drawn from a continuous population distributed on (a,b)\(\subseteq (-\infty,\infty)\). A sample quantile function is defined to be a piecewise linear interpolation of these order statistics. The method is based on the calculation of an asymptotic nonparametric confidence interval for the fractional reduction of the within-group error due to \((g+1)\)-grouping over g-grouping. The confidence interval theory (as well as the central limit theory) is developed for both universally optimal and bounded locally optimal groupings. The derivation makes use of a Donsker-type theorem for the quantile process that is also proven. The consistency of the estimators used in the proofs of the theorem is shown.
Mathematics Subject Classification ID: 62H30
Mathematics Subject Classification ID: 62G15
zbMATH DE Number: 4090609
zbMATH Keywords: M-estimator
zbMATH Keywords: quantization
zbMATH Keywords: piecewise linear interpolation of order statistics
zbMATH Keywords: universally optimal groupings
zbMATH Keywords: number of groups
zbMATH Keywords: continuous population
zbMATH Keywords: sample quantile function
zbMATH Keywords: asymptotic nonparametric confidence interval
zbMATH Keywords: within-group error
zbMATH Keywords: central limit theory
zbMATH Keywords: bounded locally optimal groupings
zbMATH Keywords: Donsker-type theorem
zbMATH Keywords: quantile process
zbMATH Keywords: consistency
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4090609