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Eigenvalues and constraints in mixture modeling: geometric and computational issues. (English) Zbl 1414.62071

Summary: 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.

MSC:

62F10 Point estimation
62F12 Asymptotic properties of parametric estimators
62F30 Parametric inference under constraints
62F35 Robustness and adaptive procedures (parametric inference)

Software:

TCLUST; mclust
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References:

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