Statistical Modeling

Simple linear models are important and relatively easy to deal with, but there are many situations where they are not appropriate. Generalized linear models make up a considerably larger class of models, which are amendable to analysis, and which cover a wide variety of important applications, such as modeling binary or polytomous data or investigating the detailed structure of higher way contingency tables. Different methods of Bootstrap estimation are considered for this class of models. Their properties are studied by comparing asymptotical results or by simulation techniques. We are now working on modifications of the nonparametric maximum-likelihood estimate in Generalized Linear Models including Models for overdispersed data, Random Effect Models and Hierarchical Models. A Bootstrap based on the respective estimating equations will be developed and will provide small sample support for the new estimating method.