Model-based clustering via new parsimonious mixtures of heavy-tailed distributions

Salvatore D. Tomarchio (), Luca Bagnato and Antonio Punzo
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Salvatore D. Tomarchio: Università degli Studi di Catania
Luca Bagnato: Università Cattolica del Sacro Cuore
Antonio Punzo: Università degli Studi di Catania

AStA Advances in Statistical Analysis, 2022, vol. 106, issue 2, No 7, 315-347

Abstract: Abstract Two families of parsimonious mixture models are introduced for model-based clustering. They are based on two multivariate distributions-the shifted exponential normal and the tail-inflated normal-recently introduced in the literature as heavy-tailed generalizations of the multivariate normal. Parsimony is attained by the eigen-decomposition of the component scale matrices, as well as by the imposition of a constraint on the tailedness parameters. Identifiability conditions are also provided. Two variants of the expectation-maximization algorithm are presented for maximum likelihood parameter estimation. Parameter recovery and clustering performance are investigated via a simulation study. Comparisons with the unconstrained mixture models are obtained as by-product. A further simulated analysis is conducted to assess how sensitive our and some well-established parsimonious competitors are to their own generative scheme. Lastly, our and the competing models are evaluated in terms of fitting and clustering on three real datasets.

Keywords: Mixture models; Parsimony; Model-based clustering; Multivariate shifted exponential normal distribution; Multivariate tail-inflated normal distribution (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10182-021-00430-8

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