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Estimating basis functions in massive fields under the spatial mixed effects model
Statistical Analysis and Data Mining ( IF 1.3 ) Pub Date : 2021-07-31 , DOI: 10.1002/sam.11537
Karl Pazdernik 1, 2 , Ranjan Maitra 3
Affiliation  

Spatial prediction is commonly achieved under the assumption of a Gaussian random field by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For massive datasets, fixed rank kriging using the expectation–maximization algorithm for estimation has been proposed as an alternative to the usual but computationally prohibitive kriging method. The method reduces computation cost of estimation by redefining the spatial process as a linear combination of basis functions and spatial random effects. A disadvantage of this method is that it imposes constraints on the relationship between the observed locations and the knots. We develop an alternative method that utilizes the spatial mixed effects model, but allows for additional flexibility by estimating the range of the spatial dependence between the observations and the knots via an alternating expectation conditional maximization algorithm. Experiments show that our methodology improves estimation without sacrificing prediction accuracy while also minimizing the additional computational burden of extra parameter estimation. The methodology is applied to a temperature dataset archived by the United States National Climate Data Center, with improved results over previous methodology.

中文翻译:

空间混合效应模型下大面积场基函数的估计

空间预测通常是在高斯随机场的假设下通过获得参数的最大似然估计来实现的,然后使用克里金方程得出预测值。对于海量数据集,已提出使用期望最大化算法进行估计的固定秩克里金法作为通常但计算量大的克里金法的替代方法。该方法通过将空间过程重新定义为基函数和空间随机效应的线性组合来降低估计的计算成本。这种方法的一个缺点是它对观察到的位置和节点之间的关系施加了限制。我们开发了一种利用空间混合效应模型的替代方法,但允许通过交替期望条件最大化算法估计观测值和结点之间的空间相关性范围来提供额外的灵活性。实验表明,我们的方法在不牺牲预测精度的情况下改进了估计,同时还最大限度地减少了额外参数估计的额外计算负担。该方法应用于美国国家气候数据中心存档的温度数据集,结果比以前的方法有所改进。
更新日期:2021-09-16
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