SEMIPARAMETRIC METHODS IN THE ESTIMATION OF TAIL PROBABILITIES AND EXTREME QUANTILES

In quantitative risk analysis, the problem of estimating small threshold exceedance probabilities and extreme quantiles arise ubiquitously in bio-surveillance, economics, natural disaster insurance actuary, quality control schemes, etc. A useful way to make an assessment of extreme events is to estimate the probabilities of exceeding large threshold values and extreme quantiles judged by interested authorities. Such information regarding extremes serves as essential guidance to interested authorities in decision making processes. However, in such a context, data are usually skewed in nature, and the rarity of exceedance of large threshold implies large fluctuations in the distribution's upper tail, precisely where the accuracy is desired mostly. Extreme Value Theory (EVT) is a branch of statistics that characterizes the behavior of upper or lower tails of probability distributions. However, existing methods in EVT for the estimation of small threshold exceedance probabilities and extreme quantiles often lead to poor predictive performance in cases where the underlying sample is not large enough or does not contain values in the distribution's tail. In this dissertation, we shall be concerned with an out of sample semiparametric (SP) method for the estimation of small threshold probabilities and extreme quantiles. The proposed SP method for interval estimation calls for the fusion or integration of a given data sample with external computer generated independent samples. Since more data are used, real as well as artificial, under certain conditions the method produces relatively short yet reliable confidence intervals for small exceedance probabilities and extreme quantiles.

A von Bertalanffy Based Model for the Estimation of Oyster (Crassostrea virginica) Growth on Restored Oyster Reefs in Chesapeake Bay

A model to estimate the mean monthly growth of Crassostrea virginica oysters in Chesapeake Bay was developed. This model is based on the classic von Bertalanffy growth function, however the growth constant is changed every monthly timestep in response to short term changes in temperature and salinity. Using a dynamically varying growth constant allows the model to capture seasonal oscillations in growth, and growth responses to changing environmental conditions that previous applications of the von Bertalanffy model do not capture. This model is further expanded to include an estimation of Perkinsus marinus impacts on growth rates as well as estimations of ecosystem services provided by a restored oyster bar over time. The model was validated by comparing growth estimates from the model to oyster shell height observations from a variety of restoration sites in the upper Chesapeake Bay. Without using the P. marinus impact on growth, the model consistently overestimates mean oyster growth. However, when P. marinus effects are included in the model, the model estimates match the observed mean shell height closely for at least the first 3 years of growth. The estimates of ecosystem services suggested by this model imply that even with high levels of mortality on an oyster reef, the ecosystem services provided by that reef can still be maintained by growth for several years. Because larger oyster filter more water than smaller ones, larger oysters contribute more to the filtration and nutrient removal ecosystem services of the reef. Therefore a reef with an abundance of larger oysters will provide better filtration and nutrient removal. This implies that if an oyster restoration project is trying to improve water quality through oyster filtration, it is important to maintain the larger older oysters on the reef.