This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
The investigator seeks to develop effective nonparametric likelihood and resampling methods for dependent or correlated data structures. The project particularly targets the development of empirical likelihood methodology for spatial data under nonstandard sampling designs, the investigation of optimal implementation of the bootstrap in non-stationary temporal and spatial settings, and the creation of novel resampling methods through data-transformations aimed at weakening data correlation. This work intends to produce efficient and accurate statistical methodology for several correlated data structures, which are applicable without stringent assumptions on the underlying data-generating process.
Scientific investigations commonly rely on the statistical analysis of data, which are often correlated in a complex manner. Current statistical metholodogy depends heavily on selecting probability models to accurately represent the underlying correlation in data. However, such model selection can be difficult in practice and any inference drawn from a mistaken model may be misleading. This research targets developing alternative, model-free tools for valid statistical inference with correlated data, which are not susceptible to errors in model choice and can also help advance data inference in scientific areas such as Environmetrics, Economics, Geology, Astronomy, etc., that naturally encounter correlated data.