Kriging for Hilbert-space valued random fields: The operatorial point of view
Kriging for Hilbert-space valued random fields: The operatorial point of view
复制标题
希尔伯特空间值随机场的克里金法：操作观点
DOI：
10.1016/j.jmva.2015.06.012
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
G. Petris
中科院分区：
文献类型：
--
作者：
A. Menafoglio;G. Petris
我们开发了一个全面的框架，线性空间预测在希尔伯特空间。本文基于Kriging的一个新的运算定义，从一个新的角度探讨了Hilbert空间中的最佳线性无偏（BLU）预测问题。我们的地面上的高斯过程在函数空间的理论和相关的概念可测线性变换的发展。我们证明，我们的新设置允许（a）导出一个显式的解决方案的问题的运算普通克里格，和（B）建立我们的新的预测与关键概念的条件期望的高斯测度的关系。我们的新理论是作为一个统一的理论克里格，其中包括克里格预测函数数据的文献中提出的有限维近似的概念。我们原来的观点克里格提供了新的相关见解，无论是有限维或无限维地理参考数据集的地质统计分析。
We develop a comprehensive framework for linear spatial prediction in Hilbert spaces. We explore the problem of Best Linear Unbiased (BLU) prediction in Hilbert spaces through an original point of view, based on a new Operatorial definition of Kriging. We ground our developments on the theory of Gaussian processes in function spaces and on the associated notion of measurable linear transformation. We prove that our new setting allows (a) to derive an explicit solution to the problem of Operatorial Ordinary Kriging, and (b) to establish the relation of our novel predictor with the key concept of conditional expectation of a Gaussian measure. Our new theory is posed as a unifying theory for Kriging, which is shown to include the Kriging predictors proposed in the literature on Functional Data through the notion of finite-dimensional approximations. Our original viewpoint to Kriging offers new relevant insights for the geostatistical analysis of either finite- or infinite-dimensional georeferenced dataset.