SEMIPARAMETRIC ESTIMATION OF A TWO-COMPONENT MIXTURE MODEL

By Laurent Bordes, Stéphane Mottelet, Pierre Vandekerkhove. 2006

166 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1dacdff17355ff43458a93c2c7b639959a308cb4

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Citations in the corpus

mixtools: An R Package for Analyzing Mixture Models (2009, background): “Both Hunter et al. (2007) and Bordes, Mottelet, and Vandekerkhove (2006) study a particular case of model (1) in which x is univariate and where φ ( · ) is a density that is assumed to be completely unspeciﬁed except that it is symmetric about zero.”
Semi-Parametric Estimation for Conditional Independence Multivariate Finite Mixture Models (2015, methodology): “[8] use the so-called minimum contrast method to estimate all of the parameters.”
Estimation of a two‐component mixture model with applications to multiple testing (2012, background): “Genovese and Wasserman (2004) showed that the estimators of α0 that were proposed by Hengartner and Stark (1995) and Swanepoel (1999) have rates of convergence {n= log.”
Semiparametric mixtures of regressions (2012, unknown): “In a non-regression context, both Bordes et al. (2006) and Hunter et al. (2007) studied univariate mixture models of the form Z ∼ m∑ j=1 λjf (z − μj), (7) where f is some symmetric density function.”
Inference in finite state space non parametric Hidden Markov Models and applications (2015, background): “However, one may not recover the individual emission distributions from a convex combination of them without further information (see e.g. Bordes et al. 2006a,b or Butucea and Vandekerkhove 2014).”
Inference for mixtures of symmetric distributions (2007, methodology): “We consider univariate, rather than multivariate, data and we achieve identifiability by imposing a symmetry restriction on the individual components; see [3] for an alternative approach to the same problem.”