Robust statistical analysis based on the generalized T distribution families

In this thesis, we consider three different forms of the generalized t distributions defined as the alternatives to the normal and the Student's t distributions in modeling data, which may have longer than normal tails, skewness, or multimodality. We investigate the existence, the uniqueness, and the robustness properties of the maximum likelihood estimators for the parameters of these distributions. We show that the maximum likelihood estimators for the parameters of the generalized t distributions can be alternative robust estimators for the location and scale estimates of a dataset. We also show that the likelihood estimating equations cannot be explicitly solved to obtain the estimates; a numerical computation method should be used to compute the estimates. To overcome the computation problem of the estimates we propose a simple iterative reweighting algorithm, and show that this algorithm is an EM algorithm. As the natural extension of the location and scale problem, the GT distribution is used as an alternative model for the error term in regression. Key Words: influence function, breakdown point, maximum likelihood, regression, EM algorithm.