Mathematical Sciences: Tests for Direction-Invariance and Separability of the Second-Order Variation of Spatial RandomFields

本研究的目的是对平稳空间随机场的一些重要性质进行统计检验。要考虑的性质是二阶变分的方向不变性（各向同性）和可分性及其变化。这些性质除了在许多情况下具有重要的科学意义外，还可以大大简化空间数据分析所涉及的计算和得出的结论。基于参数模型的半变差函数或协方差函数的参数检验方法，以及利用矩量估计方法的半参数方法的非参数检验方法也将受到关注。分析空间数据的生物、环境和物理科学家会发现测试程序很有用。本研究的目的是对平稳空间随机场的一些重要性质进行统计检验。要考虑的性质是二阶变分的方向不变性（各向同性）和可分性及其变化。这项工作将对生物、环境和物理科学领域产生潜在影响。

The objective of this research is to develop statistical tests for some important properties of stationary spatial random fields. The properties to be considered are those of direction- invariance (isotropy) and separability, and variations thereof, of the second-order variation. In addition to having important scientific meaning in many situations, these properties, when they hold, can greatly simplify both the computations involved in, and conclusions made from, the analysis of spatial data. Parametric testing approaches, which are based on a parametric model for the semivariogram or covariance function, and nonparametric approaches, which utilize method-of-moments estimators for sempiparametric approach will also receive attention. Biological environmental, and physical scientists who analyze spatial data will find the testing procedures useful. The objective of this research is to develop statistical tests for some important properties of stationary spatial random fields. The properties to be considered are those of direction- invariance (isotropy) and separability, and variations thereof, of the second-order variation. This work will have potential impact on fields of biological, environmental and physical sciences.