AI 中文总结
该研究通过Copula视角重审空间统计经典概念，讨论相关工具与模型构建，强调柯尔莫哥洛夫一致性等，整合Copula建模与空间统计多方向发展成果，为二者接口提供统一视角，涵盖统计推断及时空扩展等内容。
AI 中文摘要
空间统计通常通过二阶量（如协方差函数和变差函数）描述空间依赖性，常基于高斯随机场模型及平稳性、各向同性或基于距离的衰减等结构假设。Copulas提供了一个补充框架，将边际分布与依赖性分离，允许广泛的非高斯依赖结构。通过斯克拉定理，空间随机场的有限维分布可分解为边际和Copulas，Copulas为研究二阶总结之外的空间依赖性提供了自然语言。然而，相关文献在空间统计、Copula建模、随机过程和应用领域沿着几个基本独立的方向发展，术语和建模目标各异。本综述将这些方向整合在一起：通过Copula视角重新审视空间统计的经典概念，讨论基于Copula描述空间依赖性的工具，系统回顾空间Copula模型的构建。特别强调柯尔莫哥洛夫一致性以及为固定位置集定义的模型与真正过程级构建之间的区别。我们还讨论统计推断、时空设置的扩展以及涉及灵活边际和依赖模型的新兴方向。通过阐明现有方法之间的关系及其各自的优势和局限性，本综述为Copula建模与空间统计之间的接口提供了统一视角。
英文摘要
Spatial statistics commonly describes spatial dependence through second-order quantities such as covariance functions and variograms, often within Gaussian random-field models and under structural assumptions such as stationarity, isotropy, or distance-based decay. Copulas offer a complementary framework that separates marginal distributions from dependence and permits a broad range of non-Gaussian dependence structures. Because the finite-dimensional distributions of a spatial random field can always be decomposed into margins and copulas through Sklar's theorem, copulas provide a natural language for studying spatial dependence beyond second-order summaries. Yet the relevant literature has developed along several largely separate strands across spatial statistics, copula modeling, stochastic processes, and application domains, often with different terminology and modeling objectives. This review brings these strands together: We revisit classical concepts from spatial statistics through a copula lens, discuss copula-based tools for describing spatial dependence, and systematically review constructions of spatial copula models. Particular emphasis is placed on Kolmogorov consistency and on the distinction between models defined for a fixed set of locations and genuinely process-level constructions. We also discuss statistical inference, extensions to spatio-temporal settings, and emerging directions involving flexible marginal and dependence models. By clarifying the relationships among existing approaches and their respective strengths and limitations, the review provides a unified perspective on the interface between copula modeling and spatial statistics.
Comments21 pages
