Complex data, model selection and bootstrap inference

This project will develop and implement methodology for fitting, making inferences about and selecting statistical models for several different types of complex data. We will use the bootstrap to develop flexible, consistent methods for model selection which work well with small samples. We will explore robustness issues and develop methods which are robust against contamination and develop model-based methodology for the specific problems that arise when the data are collected in a sample survey. We will apply the methodology to the substantive motivating problems. The expected outcomes are a deeper understanding based on theoretical results and practical tools for important problems.