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 Mat\'ern 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.
翻译:在地理统计学中流行的空间过程模型通常代表观测到的数据,它是一个平稳的基本过程和白色噪音的总和。白色噪音的变化归因于测量错误或微尺度变异,被称为“小行星 ” 。我们正式根据高斯过程,在填充无症状学的框架内,根据高斯过程,即抽样规模在被捆绑的取样域内增加,确定空间模型的可识别性和一致性。我们的工作扩展了无熔岩空间模型固定域的不可测性结果。更具体地说,我们确定了Mat\'ern共变函数参数的可识别性及其最大可能性估计者在由于纳吉特造成的不连续情况下的一致性。我们还进行了模拟研究,以展示可识别数量在空间内插图中的作用。