This research will focus on five areas of environmetrics: the partitioning of spatial variability, confidence bands for interpolated random functions, quantile estimates for integrated processes, using covariate information for quantile estimation, and environmental indicies for trend estimation. In the first area, the effects of modeling the regression structure in the spatial covariance function will be assessed. In the second area, the problem is to calculate the probability that the entire field is below a specified level, conditional on the observations. The feasibility of approximating this probability with a series expansion of the conditional covariance field that is amenable to the application of Hotelling's inequality will be determined. In the third area, distributional modelling will be used to relate tail probabilities of a monthly integrated concentration process, allowing for the non-exhaustive nature of historical data. In the fourth area, extensions of Pareto tail estimators for the case of jointly distributed vector random variables will be sought. In the fifth area, methods to account for the spatial autocorrelation of separate monitoring station data will be developed. This research is in the general area of spatial statistics and is motivated by statistical problems in environmental measurement and regulation. There is increasing attention in statistics being directed at these problems involving interesting and variable dependencies among the observations. Results in this area are needed for informative policy development and sound regulation practices.
