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General estimating equations with or without bias-reducing adjustments
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General Estimating Equations with or without Bias-Reducing Adjustments (pronounced zee· bruh)

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Package description

GEEBRA is a Julia package that implements M-estimation for statistical models, either by solving estimating equations or by maximizing inference objectives, like likelihoods and composite likelihoods (see, Varin et al, 2011, for a review), using only user-specified templates of the estimating function or the objective functions contributions.

A key feature is the use of only those templates and forward mode automatic differentiation (as implemented in ForwardDiff) to provide methods for reduced-bias M-estimation (RBM-estimation; see, Kosmidis & Lunardon, 2020).

See the documentation for more information, and the examples for a showcase of the functionaly GEEBRA provides.

See for changes, bug fixes and enhancements.


Ioannis Kosmidis (author, maintainer)
Nicola Lunardon (author)


  • Varin, C., N. Reid, and D. Firth (2011). An overview of composite likelihood methods. Statistica Sinica 21(1), 5-42. Link
  • Kosmidis, I., N. Lunardon (2020). Empirical bias-reducing adjustments to estimating functions. ArXiv:2001.03786. Link
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