Semiparametric and Nonparametric Methods of Model Selection and Model Checking for Correlated Data

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Model selection and model checking are fundamental to statistical analysis. The main objective of model selection is to identify parsimonious well-fitting models in order to balance the increase in model fit against the increase in model complexity; and that of model checking is to assess or test the validity of a proposed model. An enormous amount of literature is available for independent data in this research area. For correlated data, however, there exists only fragmented work and the asymptotic theory is largely undeveloped, mainly due to (1) the lack of a rich class of models such as multivariate Gaussian for the joint distributions of the responses, (2) the complexity of the joint likelihood even when such a multivariate family of distributions is available. These obstacles make it extremely challenging, if not impossible, to apply existing model selection and model checking procedures that were developed for independent data or based on full likelihood. This project addresses this challenge by developing a set of semiparametric and nonparametric tools for model selection and model checking for correlated data, including model checking procedures based on moment conditions via the recently developed quadratic inference function and rank-based estimation equations; data-driven model checking procedures that allow for flexible alternative and increase general power performance. The large sample theory and practical performance will be investigated in depth in this project. Also on the agenda are related research issues, such as the characterization of rank regression under possible model misspecification and the theoretical robustness properties of rank-based model selection algorithms.Correlated data frequently occur in many fields, such as biomedical and health sciences, economics, social sciences and environmental studies. This work will greatly enhance the available methodologies and theories for model selection and model checking. The investigator will develop computational packages that can be easily implemented by statisticians and scientists. This project will provide scientists with new and flexible tools for analyzing high-dimensional correlated data. Education will be an important component. The research results will be incorporated at different levels of statistical courses. Undergraduate and graduate students, especially those from underrepresented groups, will be encouraged to participate in this research project.