This paper proposes a novel nonparametric approach to model and reveal differences in the geochemical properties of the soil, when these are described by space–time measurements collected in a spatial region naturally divided into two parts. The investigation is motivated by a real study on a space–time geochemical data set, consisting of measurements of potassium chloride pH, water pH, and percentage of organic carbon collected during the growing season in the agricultural and forest areas of a site near Brno (Czech Republic). These data are here modeled as spatially distributed functions of time. A permutation approach is introduced to test for the effect of covariates in a spatial functional regression model with heteroscedastic residuals. In this context, the proposed method accounts for the heterogeneous spatial structure of the data by grounding on a permutation scheme for estimated residuals of the functional model. Here, a weighted least squares model is fitted to the observations, leading to asymptotically exchangeable and, thus, permutable residuals. An extensive simulation study shows that the proposed testing procedure outperforms the competitor approaches that neglect the spatial structure, both in terms of power and size. The results of modeling and testing on the case study are shown and discussed.

中文翻译：

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存在异方差的时空地球化学数据分析的排列方法

本文提出了一种新的非参数方法来模拟和揭示土壤地球化学特性的差异，当这些差异通过在自然分为两部分的空间区域中收集的时空测量进行描述时。该调查的动机是对时空地球化学数据集的真实研究，包括测量氯化钾 pH 值、水 pH 值和生长季节期间在布尔诺附近一个地点的农业和森林地区收集的有机碳百分比（捷克共和国）。这些数据在这里被建模为时间的空间分布函数。引入了置换方法来测试协变量在具有异方差残差的空间函数回归模型中的影响。在这种情况下，所提出的方法通过基于功能模型估计残差的置换方案来解释数据的异质空间结构。在这里，加权最小二乘模型被拟合到观测值，导致渐近可交换，因此，可置换残差。一项广泛的模拟研究表明，所提出的测试程序在功率和尺寸方面都优于忽略空间结构的竞争对手方法。展示并讨论了案例研究的建模和测试结果。一项广泛的模拟研究表明，所提出的测试程序在功率和尺寸方面都优于忽略空间结构的竞争对手方法。展示并讨论了案例研究的建模和测试结果。一项广泛的模拟研究表明，所提出的测试程序在功率和尺寸方面都优于忽略空间结构的竞争对手方法。展示并讨论了案例研究的建模和测试结果。