Nonparametric Rank Based Inferences for Generalized Linear Models, Longitudinal Data Analysis, and Variable Selection

Abstract

Many relevant data sets from environmental sciences,biomedical sciences, finance, insurance, engineering, and many other disciplines have high-dimensionality, difficult to model dependence structure, outliers, and heavy tailed and asymmetric noise distribution. These challenges posed by the data require the use of robust statistical techniques in order to make reliable inferences. Many robust nonparametric statistical methods have been developed to address these challenging issues. Rank estimators are among statistical methods recently developed for this purpose. However little attention has been given to Rank estimation in Generalized Linear Models, Longitudinal Data Analysis, and Variable Selection. This dissertation proposes robust nonparametric methods based on the theory of rank for inferences in Generalized Linear Models, Longitudinal Data Analysis, and Group Variable Selection in Linear Models.