The project aims to develop accurate statistical methodology for correlated data, which applies without stringent assumptions about how data may arise. Current statistical methodology often relies on specifying an adequate model for correlated data, which can be a difficult task, and any inference drawn from a mistaken model can be unreliable. A direct benefit of this research is to provide alternative, model-free tools for statistical inference that are not susceptible to model choice and can advance data analysis in scientific areas such as environmetrics, economics, astronomy, etc., which encounter different forms of complex dependent data. Additionally, climate predictions are increasingly relevant for mitigating natural disasters and planning the use of social/economic resources. Research goals include developing new assessments of regional climate models to understand how scale differences in such models may impact climate forecasts.
The research targets development of model-free resampling and nonparametric likelihood methods for different types of dependent data structures, temporally and spatially. Three main research problems are: (1) Investigation of optimal implementations of empirical likelihood for time series (as performance is linked to tuning parameters in currently unknown ways); (2) Study of spatio-temporal resampling methods to assess the concept of "scale" in geophysical and environmental processes, with interest in evaluating regional climate models; (3) Development of new resampling methods for irregularly located spatial observations, based on data-transformations, to advance inference with spatial data. Such nonparametric methods can provide valid inference and assessments of dependence structures under mild distributional assumptions, and such methodology can also be helpful for informing model selection.
