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Estimation And Asymptotic Theory For A New Class Of Mixture Models

Author

Listed:
  • Eduardo Mendes

    (Department of Electrical Engineering, PUC-Rio)

  • Alvaro Veiga

    (Department of Electrical Engineering, PUC-Rio)

  • MArcelo Cunha Medeiros

    (Department of Economics, PUC-Rio)

Abstract

In this paper a new model of mixture of distributions is proposed, where the mixing structure is determined by a smooth transition tree architecture. Models based on mixture of distributions are useful in order to approximate unknown conditional distributions of multivariate data. The tree structure yields a model that is simpler, and in some cases more interpretable, than previous proposals in the literature. Based on the Expectation-Maximization (EM) algorithm a quasi-maximum likelihood estimator is derived and its asymptotic properties are derived under mild regularity conditions. In addition, a specific-to-general model building strategy is proposed in order to avoid possible identification problems. Both the estimation procedure and the model building strategy are evaluated in a Monte Carlo experiment, which give strong support for the theory developed in small samples. The approximation capabilities of the model is also analyzed in a simulation experiment. Finally, two applications with real datasets are considered. KEYWORDS: Mixture models, smooth transition, EM algorithm, asymptotic properties, time series, conditional distribution.

Suggested Citation

  • Eduardo Mendes & Alvaro Veiga & MArcelo Cunha Medeiros, 2007. "Estimation And Asymptotic Theory For A New Class Of Mixture Models," Textos para discussão 538, Department of Economics PUC-Rio (Brazil).
    • Handle: RePEc:rio:texdis:538
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    References listed on IDEAS

    as
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    Keywords

    mixture models; smooth transition; em algorithm; asymptotic properties; time series; conditional distribution.;
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