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On the Variance Covariance Matrix of the Maximum Likelihood Estimator of a Discrete Mixture

Author

Listed:
  • Gauthier Lanot

    (Keele University, Department of Economics)

Abstract
The estimation of models involving discrete mixtures is a common practice in econometrics, for example to account for unobserved heterogeneity. However, the literature is relatively uninformative about the measurement of the precision of the parameters. This note provides an analytical expression for the observed information matrix in terms of the gradient and hessian of the latent model when the number of components of the discrete mixture is known. This in turn allows for the estimation of the variance covariance matrix of the ML estimator of the parameters. I discuss further two possible applications of the result: the acceleration of the EM algorithm and the specification testing with the information matrix test.

Suggested Citation

  • Gauthier Lanot, 2002. "On the Variance Covariance Matrix of the Maximum Likelihood Estimator of a Discrete Mixture," Keele Economics Research Papers KERP 2002/07, Centre for Economic Research, Keele University.
    • Handle: RePEc:kee:kerpuk:2002/07
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    File URL: http://www.keele.ac.uk/depts/ec/wpapers/kerp0207.pdf
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    References listed on IDEAS

    as
    1. D. Oakes, 1999. "Direct calculation of the information matrix via the EM," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 479-482, April.
    2. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464.
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    Cited by:

    1. Hartley, Roger & Lanot, Gauthier, 2006. "Heterogeneous demand responses to discrete price changes: an application to the purchase of lottery tickets," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 859-877, February.
    2. Lanot, Gauthier & Leece, David, 2010. "The Performance of UK Securitized Subprime Mortgage Debt: ‘Idiosyncratic’ Behaviour or Mortgage Design?," MPRA Paper 27137, University Library of Munich, Germany.

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    More about this item

    Keywords

    Discrete Mixtures; EM Algorithm; Variance Covariance Matrix; Observed Information;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

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