Semiparametric estimation of a two-component mixture model

Details Semiparametric estimation of a two-component mixture model Semiparametric estimation of a two-component mixture model

2006-07-31

arxiv.org/abs/math/0607812v1

Annals of Statistics 2006, Vol. 34, No. 3, 1204-1232

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000000353 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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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