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arXiv 1908.05726math.STstat.TH
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高斯空间过程模型中块金的可辨识性和相容性

On identifiability and consistency of the nugget in Gaussian spatial process models

Wenpin Tang, Lu Zhang, Sudipto Banerjee

备注：
29 pages, 4 tables, 6 figures. This version offers some further details in the proof of Theorems 2.4 and some clarification for Theorem 2.7
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摘要：

地质统计学中流行的空间过程模型通常将观测数据表示为平滑的潜在过程和白噪声的总和。白噪声的变化归因于测量误差或微尺度变化，并且被称为“块金”。我们正式建立结果的可识别性和一致性的块金在空间模型的基础上，在填充渐近的框架内的高斯过程，即样本量增加的采样域是有界的。我们的工作扩展了无块金空间模型的固定域渐近性结果。更具体地说，我们建立的Matérn协方差函数中的参数的可识别性和一致性的最大似然估计的存在下，由于块金不连续。我们还提出了模拟研究，以证明在空间插值的可识别量的作用。

英文摘要：

Spatial process models popular in geostatistics often represent the observed data as the sum of a smooth underlying process and white noise. The variation in the white noise is attributed to measurement error, or micro-scale variability, and is called the "nugget". We formally establish results on the identifiability and consistency of the nugget in spatial models based upon the Gaussian process within the framework of in-fill asymptotics, i.e. the sample size increases within a sampling domain that is bounded. Our work extends results in fixed domain asymptotics for spatial models without the nugget. More specifically, we establish the identifiability of parameters in the Matérn covariance function and the consistency of their maximum likelihood estimators in the presence of discontinuities due to the nugget. We also present simulation studies to demonstrate the role of the identifiable quantities in spatial interpolation.

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