Some robust estimators for poisson regression models / Omnia Mohamed Saber Farghaly ; Supervised Sayed Meshaal Elsayed , Mohamed Reda Abonazel

Thesis (M.Sc.) - Cairo University - Faculty of Graduate Studies for Statistical - Department of Statistics and Econometrics

The basic Generalized Linear Models (GLM) for count data is the Poisson model, it can be estimated by maximum likelihood (ML). However, in Poisson model when the response variable is a count, its conditional variance increases more rapidly than its mean, producing a condition termed overdispersion and invalidating the use of the Poisson model. Negative binomial (NB) model with dispersion parameter to handle overdispersed count data, the quasi-Poisson model which can be estimated by the method of quasi-likelihood (QL) and other models like Generalized Poisson (GP), Conway-Maxwell Poisson (CMP), and Poisson quasi{u2011}Lindley (PQL). In addition to some methods. The zero inflated Poisson (ZIP) model may be appropriate when there are more zeroes in the data than it is consistent with a Poisson distribution, and also in zero inflated Negative Binomial (ZINB) model.Outliers are one of those statistical issues that everyone knows about, but most people aren{u2019}t sure how to deal with. Most parametric statistics, like means, standard deviations, and correlations, and every statistic based on these, are highly sensitive to outliers. Outliers can really mess up the analysis. It is well known that the ML and QL estimators for these models is very sensitive to outliers. To overcome this problem, several robust estimators for GLM have been proposed

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