Eigenvalues and constraints in mixture modeling: geometric and computational issues

Luis Angel García-Escudero (), Alfonso Gordaliza (), Francesca Greselin (), Salvatore Ingrassia () and Agustín Mayo-Iscar ()
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Luis Angel García-Escudero: University of Valladolid
Alfonso Gordaliza: University of Valladolid
Salvatore Ingrassia: University of Catania
Agustín Mayo-Iscar: University of Valladolid

Advances in Data Analysis and Classification, 2018, vol. 12, issue 2, No 3, 203-233

Abstract: Abstract This paper presents a review about the usage of eigenvalues restrictions for constrained parameter estimation in mixtures of elliptical distributions according to the likelihood approach. The restrictions serve a twofold purpose: to avoid convergence to degenerate solutions and to reduce the onset of non interesting (spurious) local maximizers, related to complex likelihood surfaces. The paper shows how the constraints may play a key role in the theory of Euclidean data clustering. The aim here is to provide a reasoned survey of the constraints and their applications, considering the contributions of many authors and spanning the literature of the last 30 years.

Keywords: Mixture model; EM algorithm; Eigenvalues; Model-based clustering; 62F10 Point estimation; 62F12 Asymptotic properties of estimators; 62F30 Inference under constraints; 62F35 Robustness and adaptive procedures (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11634-017-0293-y

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