For most of the generalized linear models (GLMs), the maximum likelihood equations involve nonlinear functions of the parameters; thus, they are intractable. Solving these equations by iterations can be problematic for reasons of slow convergence, convergence to wrong values or non-convergence of the iterations. To alleviate these difficulties we exploit modified maximum likelihood methodology into the GLMs. We provide explicit solutions that will work for all GLMs, which take account of canonical link functions. By using real life data sets, we show that the derived estimators are fully efficient for large sample sizes and highly efficient for small samples. We also study the robustness properties of these estimators under over or under-dispersion via simulations.
Keywords: Generalized Linear Models; Modified Maximum Likelihood; Robust Inference; Dispersion
Biography: Dr. Oral completed her PhD at the Hacettepe University under the guidance of Professor Moti L. Tiku from McMaster University. She became a post-doctoral fellow at the University of Washington, both in the departments of Epidemiology (September 2004-September 2005) and Biostatistics (September 2005-February 2006). During that period, she was also affiliated with the Fred Hutchinson Cancer Research Center and the Group Health Research Institute in Seattle. In 2006 she returned to Turkey to take up an assistant professorship in statistics at the Middle East Technical University. She joined LSUHSC in August 2008. Her research focuses on the area of robust statistical inference, especially in survey sampling and generalized linear models.