Semiparametric functional estimation and extreme value modeling using mixture distributions and limited quantile information

This research focuses on performing statistical inference when only a limited amount of information is available. A useful testing ground for these methods is provided by extreme value modeling. Since extreme data points are frequently scarce due to the rare nature of extreme events, the methods developed here will be demonstrated through applications involving variables with heavy-tailed distributions. The starting point will consist of a set of quantiles from the observable quantity of interest. The quantiles may be elicited from experts in some cases, they may come from previously collected data in others, or they may have originated from a combination of the two. It has been shown previously that quantiles are easier to elicit than moments as the number of quantiles grows larger. This information is then used to perform inference on the predictive space. The two primary data sets used are publicly accessible. The financial example may be found online at any site with historical daily NASDAQ returns, and the river data may be found at the United States Geological Survey website.