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Testing Independence Between Two Spatial Random Fields
Journal of Agricultural, Biological and Environmental Statistics ( IF 1.4 ) Pub Date : 2020-10-09 , DOI: 10.1007/s13253-020-00421-3
Shih-Hao Huang , Hsin-Cheng Huang , Ruey S. Tsay , Guangming Pan

In this article, we consider testing independence between two spatial Gaussian random fields evaluated, respectively, at p and q locations with sample size n, where both p and q are allowed to be larger than n. We impose no spatial stationarity and no parametric structure for the two random fields. Our approach is based on canonical correlation analysis (CCA). But instead of applying CCA directly to the two random fields, which is not feasible for high-dimensional testing considered, we adopt a dimension-reduction approach using a special class of multiresolution spline basis functions. These functions are ordered in terms of their degrees of smoothness. By projecting the data to the function space spanned by a few leading basis functions, the spatial variation of the data can be effectively preserved. The test statistic is constructed from the first sample canonical correlation coefficient in the projected space and is shown to have an asymptotic Tracy–Widom distribution under the null hypothesis. Our proposed method automatically detects the signal between the two random fields and is designed to handle irregularly spaced data directly. In addition, we show that our test is consistent under mild conditions and provide three simulation experiments to demonstrate its powers. Moreover, we apply our method to investigate whether the precipitation in continental East Africa is related to the sea surface temperature (SST) in the Indian Ocean and whether the precipitation in west Australia is related to the SST in the North Atlantic Ocean.

中文翻译:

测试两个空间随机场之间的独立性

在本文中,我们考虑在样本大小为 n 的 p 和 q 位置分别测试评估的两个空间高斯随机场之间的独立性,其中 p 和 q 都允许大于 n。我们对两个随机场没有空间平稳性和参数结构。我们的方法基于典型相关分析(CCA)。但是,不是将 CCA 直接应用于两个随机场,这对于所考虑的高维测试是不可行的,而是采用了一种使用特殊类别的多分辨率样条基函数的降维方法。这些函数按照它们的平滑度排序。通过将数据投影到由几个前导基函数跨越的函数空间,可以有效地保留数据的空间变化。检验统计量是根据投影空间中的第一个样本典型相关系数构建的,并且在原假设下具有渐近的 Tracy-Widom 分布。我们提出的方法自动检测两个随机场之间的信号,旨在直接处理不规则间隔的数据。此外,我们表明我们的测试在温和条件下是一致的,并提供了三个模拟实验来证明其能力。此外,我们应用我们的方法来研究东非大陆的降水是否与印度洋的海面温度(SST)有关,以及澳大利亚西部的降水是否与北大西洋的海温有关。
更新日期:2020-10-09
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