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Assessing Spatial Stationarity and Segmenting Spatial Processes into Stationary Components

Author

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  • ShengLi Tzeng

    (National Sun Yat-Sen University)

  • Bo-Yu Chen

    (Purdue University)

  • Hsin-Cheng Huang

    (Academia Sinica)

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.

Suggested Citation

  • ShengLi Tzeng & Bo-Yu Chen & Hsin-Cheng Huang, 2024. "Assessing Spatial Stationarity and Segmenting Spatial Processes into Stationary Components," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(2), pages 301-319, June.
    • Handle: RePEc:spr:jagbes:v:29:y:2024:i:2:d:10.1007_s13253-023-00588-5
    DOI: 10.1007/s13253-023-00588-5
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    References listed on IDEAS

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    1. Fuentes, Montserrat, 2005. "A formal test for nonstationarity of spatial stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 30-54, September.
    2. Soutir Bandyopadhyay & Suhasini Subba Rao, 2017. "A test for stationarity for irregularly spaced spatial data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 95-123, January.
    3. Zhang, Hao, 2004. "Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 250-261, January.
    4. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
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