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Maximization by Parts in Likelihood Inference


  • 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)


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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    1. repec:wsi:jecxxx:v:17:y:2009:i:01:n:s0218495809000278 is not listed on IDEAS
    2. repec:wsi:acsxxx:v:10:y:2007:i:02:n:s0219525907001045 is not listed on IDEAS

    More about this item


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

    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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