Two principal points of symmetric, strongly unimodal distributions

DOI10.1016/0167-7152(94)90012-4zbMath0799.62019OpenAlexW2053750563MaRDI QIDQ1332746

Thaddeus Tarpey

Publication date: 7 November 1994

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-7152(94)90012-4

zbMATH Keywords

principal pointsmixtures\(k\)-means clusteringconditional meansstrong unimodalityoptimal stratificationoptimal cutpointoptimal partition of distributionsself-consistent pointssymmetric, unimodal distributionwithin-group variances

Mathematics Subject Classification ID

Classification and discrimination; cluster analysis (statistical aspects) (62H30) Characterization and structure theory of statistical distributions (62E10)

Related Items (16)

Principal points analysis via p-median problem for binary data ⋮ Finding the principal points of a random variable ⋮ Principal points and elliptical distributions from the multivariate setting to the functional case ⋮ Uniqueness of principal points for univariate distributions ⋮ Uniqueness of principal points with respect to \(p\)-order distance for a class of univariate continuous distribution ⋮ A principal subspace theorem for 2-principal points of general location mixtures of spherically symmetric distributions ⋮ Principal points of a multivariate mixture distribution ⋮ An interesting property of the arcsine distribution and its applications ⋮ Optimal estimators of principal points for minimizing expected mean squared distance ⋮ On uniqueness of two principal points for univariate location mixtures ⋮ Two principal points for location mixtures ⋮ Linear Subspace Spanned by Principal Points of a Mixture of Spherically Symmetric Distributions ⋮ A parametric \(k\)-means algorithm ⋮ Model misspecification ⋮ High precision numerical computation of principal points for univariate distributions ⋮ Principal point classification: applications to differentiating drug and placebo responses in longitudinal studies

Cites Work

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• Strong consistency of k-means clustering
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• Principal points
• Note on Grouping
• On the Uniqueness of Best L 2 [ 0, 1 Approximation by Piecewise Polynomials with Variable Breakpoints]
• Optimal Grouping, Spacing, Stratification, and Piecewise Constant Approximation
• Concavity of the Log Likelihood
• Estimation of Principal Points

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