Principal points and self-consistent points of elliptical distributions

DOI10.1214/aos/1176324457zbMath0822.62042OpenAlexW2093048011MaRDI QIDQ1895346

Luning Li, Thaddeus Tarpey, Bernhard K. Flury

Publication date: 18 October 1995

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

Full work available at URL: https://doi.org/10.1214/aos/1176324457

zbMATH Keywords

normal distributionelliptical distributionsuniform distributionprincipal componentsprincipal pointsdomains of attractionself-consistent points\(k\)-means cluster analysis

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Characterization and structure theory for multivariate probability distributions; copulas (62H05)

Related Items (30)

Properties and generation of representative points of the exponential distribution ⋮ 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 ⋮ The Methods for Approximation of Principal Points for Binary Distributions on the Basis of Submodularity ⋮ Trimmed \(k\)-means: An attempt to robustify quantizers ⋮ Representative points for location-biased datasets ⋮ A principal subspace theorem for 2-principal points of general location mixtures of spherically symmetric distributions ⋮ Principal points of a multivariate mixture distribution ⋮ Minimum energy representative points ⋮ Effectiveness of a random compound noise strategy for robust parameter design ⋮ Limiting behavior of the gap between the largest two representative points of statistical distributions ⋮ Optimal estimators of principal points for minimizing expected mean squared distance ⋮ Optimal principal points estimators of multivariate distributions of location-scale and location-scale-rotation families ⋮ On uniqueness of two principal points for univariate location mixtures ⋮ Self-consistency and a generalized principal subspace theorem ⋮ Two principal points for location mixtures ⋮ On principal points for location mixtures of spherically symmetric distributions ⋮ Linear Subspace Spanned by Principal Points of a Mixture of Spherically Symmetric Distributions ⋮ Medical image compression and vector quantization ⋮ A parametric \(k\)-means algorithm ⋮ Principal points for an allometric extension model ⋮ High precision numerical computation of principal points for univariate distributions ⋮ Three kinds of discrete approximations of statistical multivariate distributions and their applications ⋮ Common principal components for dependent random vectors ⋮ Parallel principal axes ⋮ Asymptotics for trimmed \(k\)-means and associated tolerance zones. ⋮ Self-consistency: A fundamental concept in statistics ⋮ Functional quantization of Gaussian processes ⋮ On minimizing sequences for \(k\)-centres

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