Assessing Spatial Stationarity and Segmenting Spatial Processes into Stationary Components

ShengLi Tzeng, Bo-Yu Chen and Hsin-Cheng Huang ()
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ShengLi Tzeng: National Sun Yat-Sen University
Bo-Yu Chen: Purdue University
Hsin-Cheng Huang: Academia Sinica

Journal of Agricultural, Biological and Environmental Statistics, 2024, vol. 29, issue 2, No 6, 319 pages

Abstract: Abstract 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. Supplementary materials accompanying this paper appear online.

Keywords: Fused lasso; Geostatistics; Irregularly spaced data; Microergodic parameter; Nonstationary spatial process; Spatial clustering; Spatial visualization; Stationarity test; Voronoi tessellation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13253-023-00588-5

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