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.

Toxicity and Contamination in Bear Creek Sediment: Spatial Analysis and Implications for Risk Assessment

The sediments of Bear Creek near Baltimore, Maryland demonstrate substantial toxicity to benthic organisms, and contain a complex mixture of organic and inorganic contaminants. The present study maps the spatial extent and depth profile of toxicity and contamination in Bear Creek, and explores correlations between heavy metals, organic contaminants, and toxic responses. Two novel analytical techniques – handheld XRF and an antibody-based PAH biosensor – were applied to samples from the site to quantify total metals and total PAHs in sediments. By comprehensively assessing toxicity in Bear Creek, the present study provides data to inform future risk assessments and management decisions relating for the site, while demonstrating the benefits of applying joint biological assays and chemical assessment methods to sediments with complex contaminant mixtures.