Mixed Domain Asymptotics for Geostatistical Processes
Mixed Domain Asymptotics for Geostatistical Processes
复制标题
地统计过程的混合域渐近
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Tingjin Chu
中科院分区：
文献类型：
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作者：
Tingjin Chu
地统计学是空间统计学的三个主要分支之一，极大似然方法被广泛用于参数估计。极大似然估计量的渐近性质通常是在递增域渐近框架或填充渐近框架下考虑的。第三种框架是混合域渐近框架，其优点是结合了协方差结构的局部和全局性质。在混合域渐近框架下，我们建立了极大似然估计的渐近性质。除渐近框架外，抽样设计和协方差函数的形式也是影响极大似然估计渐近性质的重要因素。本文给出了保证这些估计量的相合性和渐近正态性的一般条件。对一些常用的协方差函数验证了所加条件。所得到的渐近性为混合域渐近下参数估计的收敛速率提供了新的见解，并为实际数据分析提供了一些有用的指导。为了检验最大似然估计的有限样本特性，进行了模拟研究，并分析了年降水异常数据集进行说明。
Geostatistics is one of the three main branches of spatial statistics, with the maximum likelihood method is widely used for parameter estimation. The asymptotic properties of maximum likelihood estimators are often considered under the increasing domain asymptotic framework or the infill asymptotic framework. A third framework, the mixed domain asymptotic framework, has the advantage of incorporating both local and global properties of the covariance structure. In this study, we establish the asymptotic properties of maximum likelihood estimators under the mixed domain asymptotic framework. In addition to the asymptotic framework, the sampling design and the form of the covariance functions are also important factors for the asymptotic properties of maximum likelihood estimators. Here, general conditions are imposed to ensure the consistency and asymptotic normality of these estimators. The imposed conditions are verified for some commonly used covariance functions. The resulting asymptotics provides novel insights into the convergence rates of parameter estimators under mixed domain asymptotics, as well as some useful guidelines for data analysis in practice. Simulation studies are conducted to examine the finite-sample properties of maximum likelihood estimators, and a yearly precipitation anomaly data set is analyzed for illustration.