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Estimation Theory for Generalized Linear Models

In: Future Perspectives in Risk Models and Finance

Author

Listed:
  • Alain Bensoussan

    (University of Texas at Dallas)

  • Pierre Bertrand

    (Université Clermont-Ferrand 2)

  • Alexandre Brouste

    (Université du Maine)

Abstract

Generalized Linear Models have been introduced by (Nelder and Wedderburn 1972). See also the book (McCullagh and Nelder 1983). They describe random observations depending on unobservable variables of interest, generalizing the standard gaussian error model. Many estimation results can be obtained in this context, which generalize with some approximation procedures the gaussian case. We revisit and extend the results. In particular, we prove the cental limit theorem for the MLE, maximum likelihood estimator, in a general setting. We also provide a recursive estimator, similar to the Kalman filter. We also consider dynamic models and develop several methods, including that of (West et al. 1985).

Suggested Citation

  • Alain Bensoussan & Pierre Bertrand & Alexandre Brouste, 2015. "Estimation Theory for Generalized Linear Models," International Series in Operations Research & Management Science, in: Alain Bensoussan & Dominique Guegan & Charles S. Tapiero (ed.), Future Perspectives in Risk Models and Finance, edition 127, pages 1-69, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-07524-2_1
    DOI: 10.1007/978-3-319-07524-2_1
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