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Maximization by Parts in Likelihood Inference

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Author Info

  • Peter X.-K. Song

    ()
    (Department of Mathematics and Statistics, York University; Toronto, ON)

  • Yanqin Fan

    ()
    (Department of Economics, Vanderbilt University)

  • John D. Kalbfleisch

    ()
    (Department of Biostatistics, University of Michigan School of Public Health)

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    Abstract

    This paper presents and examines a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest. The method circumvents the need to compute second order derivatives of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log likelihood from a simply analyzed model and the second part is used to update estimates from the first. Convergence properties of this fixed point algorithm are examined and asymptotics are derived for estimators obtained by using only a finite number of steps. Illustrative examples considered in the paper include bivariate and multivariate Gaussian copula models, nonnormal random effects and state space models. Properties of the algorithm and of estimators are evaluated in simulation studies on a bivariate copula model and a nonnormal linear random effects model.

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    File URL: http://www.accessecon.com/pubs/VUECON/vu03-w19.pdf
    File Function: First version, 2003
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    Bibliographic Info

    Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0319.

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    Date of creation: Sep 2003
    Date of revision:
    Handle: RePEc:van:wpaper:0319

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    Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

    Related research

    Keywords: Copula models; fixed-point algorithm; information dominance; iterative algorithm; nonnormal random effects; score equation; state space models;

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    1. Verbeke, Geert & Lesaffre, Emmanuel, 1997. "The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 23(4), pages 541-556, February.
    2. Luc Bauwens & David Veredas, 2004. "The stochastic conditional duration model: a latent factor model for the analysis of financial durations," ULB Institutional Repository 2013/136234, ULB -- Universite Libre de Bruxelles.
    3. Peter Xue-Kun Song, 2000. "Multivariate Dispersion Models Generated From Gaussian Copula," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 27(2), pages 305-320.
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