Maximum likelihood estimation of generalized linear models with generalized Gaussian residuals

Abstract

Assumption of normally distributed residuals is one of the big challenges in the generalized linear models (GLM). Recently, generalized Gaussian distribution (GGD) is used widely to analyze and model heavy-tail signals. Consequently, investigations for robust estimation of regression coefficients have led us to introduce GG-GLM, which models the GLM residuals using GGD. This model can deal with broad range of residuals distributions that have lower or heavier tailed behavior than the Gaussian distribution. The model parameters are estimated by a maximum likelihood (ML) approach. Experimental results on the synthetic data confirms the superior performance of GG-GLM model in comparison with the GLM model during the heavy tailed behavior of data.