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Statistics > Methodology arXiv:1911.02249 (stat) [Submitted on 6 Nov 2019 ( v1 ), last revised 7 Nov 2019 (this version, v2)] Title: Estimation of Spatial Deformation for Nonstationary Processes via Variogram Alignment Authors: Ghulam A. Qadir , Ying Sun , Sebastian Kurtek View a PDF of the paper titled Estimation of Spatial Deformation for Nonstationary Processes via Variogram Alignment, by Ghulam A. Qadir and 2 other authors View PDF HTML (experimental) Abstract: In modeling spatial processes, a second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space, leading to a heterogeneous spatial dependence structure, therefore requiring nonstationary modeling. Spatial deformation is one of the main methods for modeling nonstationary processes, assuming the nonstationary process has a stationary counterpart in the deformed space. The estimation of the deformation function poses severe challenges. Here, we introduce a novel approach for nonstationary geostatistical modeling, using space deformation, when a single realization of the spatial process is observed. Our method is based, at a fundamental level, on aligning regional variograms, where warping variability of the distance from each subregion explains the spatial nonstationarity. We propose to use multi-dimensional scaling to map the warped distances to spatial locations. We asses the performance of our new method using multiple simulation studies. Additionally, we illustrate our methodology on precipitation data to estimate the heterogeneous spatial dependence and to perform spatial predictions. Subjects: Methodology (stat.ME) ; Applications (stat.AP) MSC classes: 62H11, 62M30 Cite as: arXiv:1911.02249 [stat.ME] (or arXiv:1911.02249v2 [stat.ME] for this version) https://doi.org/10.48550/arXiv.1911.02249 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Technometrics 2021 Related DOI : https://doi.org/10.1080/00401706.2021.1883481 Focus to learn more DOI(s) linking to related resources Submission history From: Ghulam Abdul Qadir [ view email ] [v1] Wed, 6 Nov 2019 08:33:28 UTC (1,239 KB) [v2] Thu, 7 Nov 2019 09:01:11 UTC (4,406 KB) Full-text links: Access Paper: View a PDF of the paper titled Estimation of Spatial Deformation for Nonstationary Processes via Variogram Alignment, by Ghulam A. Qadir and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: stat.ME < prev | next > new | recent | 2019-11 Change to browse by: stat stat.AP References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? )