Parsimony and parameter estimation for mixtures of multivariate leptokurtic-normal distributions

Mixtures of multivariate leptokurtic-normal distributions have been recently introduced in the clustering literature based on mixtures of elliptical heavy-tailed distributions. They have the advantage of having parameters directly related to the moments of practical interest. We derive two estimatio...

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Bibliographic Details
Published in:Advances in data analysis and classification Vol. 18; no. 3; pp. 597 - 625
Main Authors: Browne, Ryan P., Bagnato, Luca, Punzo, Antonio
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2024
Springer Nature B.V
Subjects:
Algorithms
Chemistry and Earth Sciences
Clustering
Computer Science
Data Mining and Knowledge Discovery
Economics
Finance
Fixed points (mathematics)
Health Sciences
Humanities
Insurance
Kurtosis
Law
Management
Mathematics and Statistics
Medicine
Mixtures
Multivariate analysis
Parameter estimation
Physics
Regular
Regular Article
Simulation
Statistical Theory and Methods
Statistics
Statistics for Business
Statistics for Engineering
Statistics for Life Sciences
Statistics for Social Sciences
Leptokurtic-normal distribution
Mixture models
Parsimony
Majorization–minimization algorithm
62Hxx Multivariate analysis
62H12 Estimation in multivariate analysis
62G07 Density estimation
62H30 Classification and discrimination; cluster analysis (statistical aspects); mixture models
ISSN:1862-5347, 1862-5355
Online Access:Get full text
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Summary:Mixtures of multivariate leptokurtic-normal distributions have been recently introduced in the clustering literature based on mixtures of elliptical heavy-tailed distributions. They have the advantage of having parameters directly related to the moments of practical interest. We derive two estimation procedures for these mixtures. The first one is based on the majorization-minimization algorithm, while the second is based on a fixed point approximation. Moreover, we introduce parsimonious forms of the considered mixtures and we use the illustrated estimation procedures to fit them. We use simulated and real data sets to investigate various aspects of the proposed models and algorithms.
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ISSN:1862-5347
1862-5355
DOI:10.1007/s11634-023-00558-2