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On robustness of maximum likelihood estimates for Poisson-lognormal models

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  • Weems, K. S.
  • Smith, P. J.

Abstract

Mixed Poisson regression models, a class of generalized linear mixed models, are commonly used to analyze count data that exhibit overdispersion. Because inference for these models can be computationally difficult, simplifying distributional assumptions are often made. We consider an influence function representing effects of infinitesimal perturbations of the mixing distribution. This function enables us to compute Gâteaux derivatives of maximum likelihood estimates (MLEs) under perturbations of the mixing distribution for Poisson-lognormal models. Provided the first two moments exist, these MLEs are robust in the sense that their Gâteaux derivatives are bounded.

Suggested Citation

  • Weems, K. S. & Smith, P. J., 2004. "On robustness of maximum likelihood estimates for Poisson-lognormal models," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 189-196, January.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:2:p:189-196
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    References listed on IDEAS

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    1. White, Halbert, 1980. "Nonlinear Regression on Cross-Section Data," Econometrica, Econometric Society, vol. 48(3), pages 721-746, April.
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    Cited by:

    1. Kimberly S. Weems & Paul J. Smith, 2018. "Assessing the robustness of estimators when fitting Poisson inverse Gaussian models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(8), pages 985-1004, November.

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