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

本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带、综合过程的分位数估计、使用协变量信息进行分位数估计和趋势估计的环境指数。在第一个领域，将评估空间协方差函数中回归结构建模的效果。在第二个领域，问题是计算整个领域低于指定水平的概率，这取决于观测结果。用条件协方差场的级数展开式逼近该概率的可行性，并确定其适用于霍特林不等式的应用。在第三个领域，将使用分布模型来关联每月综合浓度过程的尾部概率，从而考虑到历史数据的非详尽性。在第四部分，将寻求联合分布向量随机变量情况下Pareto尾估计的扩展。在第五个领域，将开发考虑单独监测站数据空间自相关的方法。这项研究是在空间统计的一般领域，是由环境测量和调节的统计问题的动机。在统计学中，越来越多的人关注这些问题，这些问题涉及观察结果之间有趣的和可变的依赖关系。这一领域的成果是制定翔实的政策和健全的监管实践所必需的。

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.