Estimation Theory for Generalized Linear Models

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).

Also with the College of Science and Engineering, Systems Engineering and Engineering Management, City University Hong Kong. Research supported by the National Science Foundation under grant DMS-1303775 and the Research Grants Council of the Hong Kong Special Administrative Region (CityU 500113).