In this research, we propose a novel technique for visualizing nonstationarity in geostatistics, particularly when confronted with a single realization of data at irregularly spaced locations. Our method hinges on formulating a statistic that tracks a stable microergodic parameter of the exponential covariance function, allowing us to address the intricate challenges of nonstationary processes that lack repeated measurements. We implement the fused lasso technique to elucidate nonstationary patterns at various resolutions. For prediction purposes, we segment the spatial domain into stationary sub-regions via Voronoi tessellations. Additionally, we devise a robust test for stationarity based on contrasting the sample means of our proposed statistics between two selected Voronoi subregions. The effectiveness of our method is demonstrated through simulation studies and its application to a precipitation dataset in Colorado.

翻译：在本研究中，我们提出了一种用于可视化地统计学中非平稳性的新技术，尤其适用于在位置不规则分布的单一数据实现场景下。该方法基于构建一个跟踪指数协方差函数稳定微遍历参数的统计量，从而应对缺乏重复测量的非平稳过程所涉及的复杂挑战。我们采用融合套索技术以不同分辨率揭示非平稳模式。为进行预测，我们通过Voronoi镶嵌将空间域分割为平稳子区域。此外，我们设计了一种稳健的平稳性检验方法，通过对比两个选定Voronoi子区域的样本均值差异来实现。通过模拟研究及其在科罗拉多州降水数据集上的应用，验证了该方法的有效性。