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An approximation to the information matrix of exponential family finite mixtures

Author

Listed:
  • Andrew M. Raim

    (University of Maryland, Baltimore County
    Center for Statistical Research and Methodology, U.S. Census Bureau)

  • Nagaraj K. Neerchal

    (University of Maryland, Baltimore County)

  • Jorge G. Morel

    (University of Maryland, Baltimore County)

Abstract

A simple closed form of the Fisher information matrix (FIM) usually cannot be obtained under a finite mixture. Several authors have considered a block-diagonal FIM approximation for binomial and multinomial finite mixtures, used in scoring and in demonstrating relative efficiency of proposed estimators. Raim et al. (Stat Methodol 18:115–130, 2014a) noted that this approximation coincides with the complete data FIM of the observed data and latent mixing process jointly. It can, therefore, be formulated for a wide variety of missing data problems. Multinomial mixtures feature a number of trials, which, when taken to infinity, result in the FIM and approximation becoming arbitrarily close. This work considers a clustered sampling scheme which allows the convergence result to be extended significantly to the class of exponential family finite mixtures. A series of examples demonstrate the convergence result and suggest that it can be further generalized.

Suggested Citation

  • Andrew M. Raim & Nagaraj K. Neerchal & Jorge G. Morel, 2017. "An approximation to the information matrix of exponential family finite mixtures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 333-364, April.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:2:d:10.1007_s10463-015-0542-9
    DOI: 10.1007/s10463-015-0542-9
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    References listed on IDEAS

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    1. Neerchal, Nagaraj K. & Morel, Jorge G., 2005. "An improved method for the computation of maximum likeliood estimates for multinomial overdispersion models," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 33-43, April.
    2. Boldea, Otilia & Magnus, Jan R., 2009. "Maximum Likelihood Estimation of the Multivariate Normal Mixture Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1539-1549.
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