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Abstract Details

Activity Number: 659
Type: Contributed
Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
Sponsor: Biometrics Section
Abstract - #306739
Title: Stochastic and Nonstochastic Explanatory Variables in Generalized Linear Models
Author(s): Evrim Oral*+
Companies: Louisiana State University Health Sciences Center
Address: 2020 Gravier Street, 3rd Floor, New Orleans , LA, 70112, USA
Keywords: Generalized Linear Models ; Exponential Family ; Maximum Likelihood ; Robustness ; Relative Efficiency
Abstract:

The maximum likelihood equations are generally intractable and, therefore, the maximum likelihood estimators are elusive. To rectify this situation, Tiku (1967) developed the method of modified maximum likelihood (MML) estimation. The method is now well established and gives estimators which are simple and highly efficient. Tiku and Vaughan (1997) used the method to extend the techniques of binary regression to non-logistic density functions considering a nonstochastic independent variable. In this study we extend their work to generalized linear models (GLM). We derive a single expression for the MML estimators which are valid for most GLM such as Gamma or Inverse Gaussian regression models, and study their properties. We also introduce a stochastic explanatory variable into the GLM which is a very realistic situation in most practical applications. We derive the MML estimators and study their efficiency and robustness properties. The results obtained are enormously superior to those confined to nonstochastic covariates. The applications of the techniques are illustrated by authentic real-life data.


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