College of Liberal Arts
This work focuses on studying large sample properties of nonparametric statistical procedures. Many of the procedures involve a so-called shape constraint. It is often preferable to use flexible nonparametric methods, rather than restrictive parametric ones, so that estimation and inference yield reliable results without depending on strong assumptions. Unfortunately, most classical nonparametric methods rely heavily on selecting correctly (potentially many) tuning parameter(s). Selecting them well can be challenging, especially in multivariate settings.
These researchers focus mostly on methods that incorporate so-called shape constraints. One of the major benefits to using shape constraints is that they are nonparametric, so they are flexible, yet often they do not require tuning parameter selection. This work requires many large-scale simulation studies; each new procedure is tested on a battery of models from which the researchers can simulate data and see how the procedure performs. Thus computing is a crucial part of the work.