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Maximization by Parts in Likelihood Inference

Author

Listed:
  • 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)

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.

Suggested Citation

  • Peter X.-K. Song & Yanqin Fan & John D. Kalbfleisch, 2003. "Maximization by Parts in Likelihood Inference," Vanderbilt University Department of Economics Working Papers 0319, Vanderbilt University Department of Economics.
    • Handle: RePEc:van:wpaper:0319
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    File URL: http://www.accessecon.com/pubs/VUECON/vu03-w19.pdf
    File Function: First version, 2003
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    Citations

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    Cited by:

    1. Zhi Tang & Sandra Rothenberg, 2009. "Does Perceptual Acuity Matter? — An Investigation Of Entrepreneurial Orientation, Perceptual Acuity, And Firm Performance," Journal of Enterprising Culture (JEC), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 79-102.
    2. Jinqing Fang & Qiao Bi & Yong Li & Xin-Biao Lu & Qiang Liu, 2007. "Toward A Harmonious Unifying Hybrid Model For Any Evolving Complex Networks," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 117-141.

    More about this item

    Keywords

    Copula models; fixed-point algorithm; information dominance; iterative algorithm; nonnormal random effects; score equation; state space models;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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