Inconsistent estimation and asymptotically equal interpolations in model-based geostatistics
Inconsistent estimation and asymptotically equal interpolations in model-based geostatistics
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DOI：
10.1198/016214504000000241
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发表时间：
2004-03-01
影响因子：
3.7
通讯作者：
Zhang, H
中科院分区：
文献类型：
--
作者：
Zhang, H
它表明，在基于模型的地质统计学，不是所有的参数在Matern类可以一致地估计，如果数据在一个固定的域中观察到的密度增加，无论使用的估计方法。然而，最大似然方法可以一致地估计一个量，并且该量对于空间插值更重要。利用概率测度的等价性和正交性建立了相应的结果。给出了高斯等价测度和非高斯等价测度的充分条件，以及高斯等价测度的必要条件。两个模拟研究表明，固定域的渐近性质可以解释一些有限样本行为的插值和估计时，样本容量是适度的大。
it is shown that in model-based geostatistics, not all parameters in the Matern class can be estimated consistently if data are observed in an increasing density in a fixed domain, regardless of the estimation methods used. Nevertheless, one quantity can be estimated consistently by the maximum likelihood method, and this quantity is more important to spatial interpolation. The results are established by using the properties of equivalence and orthogonality of probability measures. Some sufficient conditions are provided for both Gaussian and non-Gaussian equivalent measures, and necessary conditions are provided for Gaussian equivalent measures. Two simulation studies are presented that show that the fixed-domain asymptotic properties can explain some finite-sample behavior of both interpolation and estimation when the sample size is moderately large.