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June 2006 Semiparametric estimation of a two-component mixture model
Laurent Bordes, Stéphane Mottelet, Pierre Vandekerkhove
Ann. Statist. 34(3): 1204-1232 (June 2006). DOI: 10.1214/009053606000000353


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.


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Laurent Bordes. Stéphane Mottelet. Pierre Vandekerkhove. "Semiparametric estimation of a two-component mixture model." Ann. Statist. 34 (3) 1204 - 1232, June 2006.


Published: June 2006
First available in Project Euclid: 10 July 2006

zbMATH: 1112.62029
MathSciNet: MR2278356
Digital Object Identifier: 10.1214/009053606000000353

Primary: 62G05 , 62G20
Secondary: 62E10

Keywords: consistency , contrast estimators , Identifiability , mixing operator , rate of convergence , semiparametric , two-component mixture model

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 3 • June 2006
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