Maximum likelihood estimation of heterogeneous mixtures of Gaussian and uniform distributions. (English) Zbl 1203.62017

Summary: Existence and consistency of maximum likelihood estimators of the parameters of heterogeneous mixtures of Gaussian and uniform distributions with known number of components are shown under constraints to prevent the likelihood from degeneration and to ensure identifiability. The EM-algorithm is discussed, and for the special case with a single uniform component a practical scheme to find a good local optimum is proposed. The method is compared theoretically and empirically to the estimation of a Gaussian mixture with “noise component” as introduced by J. D. Banfield and A. E. Raftery [Biometrics 49, No. 3, 803–821 (1993; Zbl 0794.62034)] to find out whether it is a worthwhile alternative particularly in situations with outliers and points not belonging to the Gaussian components.


62F10 Point estimation
65C60 Computational problems in statistics (MSC2010)
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62F12 Asymptotic properties of parametric estimators


Zbl 0794.62034


Full Text: DOI


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