The Annals of Statistics

Semiparametric estimation of a two-component mixture model

Laurent Bordes, Stéphane Mottelet, and Pierre Vandekerkhove

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Suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter. Such a model is known to be nonidentifiable from a nonparametric viewpoint. However, if we assume that the unknown mixed distribution is symmetric, we obtain the identifiability of this model, which is then defined by four unknown parameters: the mixing proportion, two location parameters and the cumulative distribution function of the symmetric mixed distribution. We propose estimators for these four parameters when no training data is available. Our estimators are shown to be strongly consistent under mild regularity assumptions and their convergence rates are studied. Their finite-sample properties are illustrated by a Monte Carlo study and our method is applied to real data.

Article information

Ann. Statist., Volume 34, Number 3 (2006), 1204-1232.

First available in Project Euclid: 10 July 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G20: Asymptotic properties
Secondary: 62E10: Characterization and structure theory

Semiparametric two-component mixture model identifiability contrast estimators consistency rate of convergence mixing operator


Bordes, Laurent; Mottelet, Stéphane; Vandekerkhove, Pierre. Semiparametric estimation of a two-component mixture model. Ann. Statist. 34 (2006), no. 3, 1204--1232. doi:10.1214/009053606000000353.

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