论文标题
在空间统计中统一的紧凑支持和母子协方差功能
Unifying Compactly Supported and Matern Covariance Functions in Spatial Statistics
论文作者
论文摘要
数十年来，MAT {é} RN家族在空间统计中起着核心作用，是一个灵活的参数类，其中一个参数确定了基础空间场的路径的平滑度。 本文提出了一个新的空间协方差函数家族，这源于广义温德兰家族的重新聚集。至于垫子{é} rn情况，新类允许连续参数化基础高斯随机场的平滑度，并由紧凑的支持。 更重要的是，我们表明，提出的协方差家庭概括了作为特殊限制案例获得的垫子{é} rn模型。我们的理论结果的实际含义疑问，从建模和计算角度来看，垫子{é} rn协方差的有效灵活性。 我们的数值实验阐明了提出的模型与垫子{é} RN模型的收敛速度。我们还检查了相关（逆）协方差矩阵的稀疏水平以及在增加和固定域渐近性下的最大似然估计器的渐近分布。通过在美国东南部的最高温度上分析一个地理学数据集，并对大型空间点引用了年度总降水异常的数据集，来说明我们提案的有效性
The Mat{é}rn family of covariance functions has played a central role in spatial statistics for decades, being a flexible parametric class with one parameter determining the smoothness of the paths of the underlying spatial field. This paper proposes a new family of spatial covariance functions, which stems from a reparameterization of the generalized Wendland family. As for the Mat{é}rn case, the new class allows for a continuous parameterization of the smoothness of the underlying Gaussian random field, being additionally compactly supported. More importantly, we show that the proposed covariance family generalizes the Mat{é}rn model which is attained as a special limit case. The practical implication of our theoretical results questions the effective flexibility of the Mat{é}rn covariance from modeling and computational viewpoints. Our numerical experiments elucidate the speed of convergence of the proposed model to the Mat{é}rn model. We also inspect the level of sparseness of the associated (inverse) covariance matrix and the asymptotic distribution of the maximum likelihood estimator under increasing and fixed domain asymptotics. The effectiveness of our proposal is illustrated by analyzing a georeferenced dataset on maximum temperatures over the southeastern United States, and performing a re-analysis of a large spatial point referenced dataset of yearly total precipitation anomalies
