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\noindent Statistica Sinica {\bf 16}(2006), 153-163

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\centerline{\large\bf SEMI-PARAMETRIC INFERENCE IN A BIVARIATE}
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\centerline{\large\bf  (MULTIVARIATE) MIXTURE MODEL}
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\author{Denis Heng-Yan Leung and Jing Qin}
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\centerline{\it Singapore Management University and}
\centerline{\it National Institute of
Allergy and Infectious Diseases}
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\begin{quotation}
\noindent {\it Abstract:}
We consider estimation in a bivariate mixture model in which the
component distributions can be decomposed into identical distributions.
Previous approaches to estimation involve parametrizing the distributions.
In this paper, we use a semi-parametric approach. The method is based on the
exponential tilt model of Anderson (1979), where the log ratio of probability
(density) functions from the bivariate components is linear in the observations.
The proposed model does not require training samples, i.e., data with confirmed
component membership. We show that in bivariate mixture models, parameters are
identifiable. This is in contrast to previous works, where parameters are identifiable
if and only if each univariate marginal model is identifiable (Teicher (1967)).\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Empirical likelihood, multivariate mixture, semi-parametric, Shannon's mutual information.\par
\end{quotation}

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