Mathematical Sciences: Statistics and Environmental Factors in Health (SEFH): Statistical Problems in Environmental Measurement and Regulation

这项研究将集中在环境计量学的五个领域：空间变异性的划分，内插随机函数的置信度范围，综合过程的分位数估计，使用协变量信息进行分位数估计，以及环境指数用于趋势估计。在第一个领域中，将评估在空间协方差函数中对回归结构进行建模的效果。在第二个区域，问题是根据观测结果计算整个油田低于指定水平的概率。将确定用服从霍特林不等式应用的条件协方差场的级数展开来近似该概率的可行性。在第三个领域，将使用分布模型来联系每月综合集中过程的尾部概率，从而考虑到历史数据的非穷尽性。在第四个领域，将寻求联合分布向量随机变量情况下的Pareto尾部估计的推广。在第五个领域，将开发独立监测站数据的空间自相关性的解释方法。这项研究属于空间统计学的一般领域，其动机是环境测量和监管中的统计问题。统计学越来越关注这些问题，这些问题涉及观测之间有趣的和可变的相关性。这一领域的成果对于信息政策的制定和健全的监管做法是必要的。

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.