Optimal estimators of principal points for minimizing expected mean squared distance

DOI10.1016/J.JSPI.2015.05.005zbMath1326.62123OpenAlexW1948404763MaRDI QIDQ897631

Thaddeus Tarpey, Hiroshi Kurata, Shun Matsuura

Publication date: 7 December 2015

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2015.05.005

zbMATH Keywords

normal distributionelliptical distributions\(k\)-means clusteringlocation-scale family\(t\)-distributionself-consistencyprincipal curves and surfaces

Mathematics Subject Classification ID

Multivariate analysis (62H99) Estimation in multivariate analysis (62H12) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items (6)

Properties and generation of representative points of the exponential distribution ⋮ Optimal quantization for the Cantor distribution generated by infinite similutudes ⋮ Bayes estimator of process capability index C_pk with a specified prior mean ⋮ Optimal principal points estimators of multivariate distributions of location-scale and location-scale-rotation families ⋮ Unnamed Item ⋮ High precision numerical computation of principal points for univariate distributions

Uses Software

• Flury
• AS 136
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Cites Work

• Unnamed Item
• Unnamed Item
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• Algorithm AS 136: A K-Means Clustering Algorithm
• Partitioning of functional data for understanding heterogeneity in psychiatric conditions
• A principal subspace theorem for 2-principal points of general location mixtures of spherically symmetric distributions
• Principal points of a multivariate mixture distribution
• Principal points for an allometric extension model
• Principal points and elliptical distributions from the multivariate setting to the functional case
• Computational intelligence paradigms. Innovative applications
• On principal points for location mixtures of spherically symmetric distributions
• Allometric extension model for conditional distributions
• Principal point classification: applications to differentiating drug and placebo responses in longitudinal studies
• Strong consistency of k-means clustering
• Two principal points of symmetric, strongly unimodal distributions
• Self-consistent patterns for symmetric multivariate distributions
• Self-consistency: A fundamental concept in statistics
• Clustering functional data
• Principal points and self-consistent points of symmetric multivariate distributions
• Principal points and self-consistent points of elliptical distributions
• Classification performance resulting from a 2-means
• On uniqueness of two principal points for univariate location mixtures
• Foundations of quantization for probability distributions
• A parametric \(k\)-means algorithm
• Linear Subspace Spanned by Principal Points of a Mixture of Spherically Symmetric Distributions
• Principal points
• Note on Grouping
• An asymptotic result on principal points for univariate distributions
• Sufficient conditions for uniqueness of a locally optimal quantizer for a class of convex error weighting functions
• Printer graphics for clustering
• METHODS FOR ESTIMATING PRINCIPAL POINTS
• TWO PRINCIPAL POINTS FOR MULTIVARIATE LOCATION MIXTURES OF SPHERICALLY SYMMETRIC DISTRIBUTIONS
• Allometric Extension
• Quantization
• Principal Curves
• Estimation of Principal Points
• Optimal Partitioning for Linear Mixed Effects Models: Applications to Identifying Placebo Responders
• Modified Liu-Type Estimator Based on (r − k) Class Estimator
• A Property of Maximum Likelihood Estimators of Location and Scale Parameters
• Some characterizations of symmetric two-principal points

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