Estimation Theory for Generalized Linear Models

Alain Bensoussan (), Pierre Bertrand and Alexandre Brouste
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Alain Bensoussan: University of Texas at Dallas
Pierre Bertrand: Université Clermont-Ferrand 2
Alexandre Brouste: Université du Maine

A chapter in Future Perspectives in Risk Models and Finance, 2015, pp 1-69 from Springer

Abstract: 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).

Keywords: Probability Density; Link Function; Conditional Probability; Kalman Filter; Weibull Distribution (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-3-319-07524-2_1

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DOI: 10.1007/978-3-319-07524-2_1

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