A robust maximum likelihood estimation approach for Ordinary Kriging with outlier-contaminated spatial data.
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| Title: | A robust maximum likelihood estimation approach for Ordinary Kriging with outlier-contaminated spatial data. |
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| Authors: | Yildirim, Vural1 (AUTHOR) vurall_yildirim@hotmail.com, Todini, Ezio2 (AUTHOR) presidente-onorario@sii-ihs.it, Kantar, Yeliz Mert3 (AUTHOR) ymert@eskisehir.edu.tr |
| Source: | Environmental & Ecological Statistics. Mar2026, Vol. 33 Issue 1, p513-544. 32p. |
| Subject Terms: | Kriging, Robust statistics, Variograms, Outliers (Statistics), Maximum likelihood statistics, Spatial data structures, Geographic spatial analysis, Monte Carlo method |
| Abstract: | Ordinary Kriging is a popular geostatistical technique for spatial interpolation and prediction. However, classical maximum likelihood estimation (MLE) of variogram parameters is known to be sensitive to outliers, resulting in biased variogram models and poor prediction performance. This study proposes a more robust MLE framework that reduces the influence of outliers while retaining the essential spatial dependence structure. Expanding on Todini and Ferraresi (1996) formulation of Kriging, robust statistical methods are incorporated into the estimation procedure, allowing for stable inference in the presence of outlier-contaminated spatial data. The proposed approach is analytically developed, and its properties are investigated using extensive Monte Carlo simulations. The practical relevance of this method is demonstrated by applying it to a real-world nitrogen dioxide (NO2) dataset. Conventional methods such as MLE, least squares, and weighted least squares estimation do not adequately capture spatial variation due to outliers. The results show that the proposed robust method improves parameter estimates and makes more reliable predictions, especially in scenarios with outlier-contaminated spatial data. These findings emphasize the importance of robust inference for Kriging's environmental applications. [ABSTRACT FROM AUTHOR] |
| Copyright of Environmental & Ecological Statistics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | GreenFILE |
| FullText | Text: Availability: 0 |
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| Header | DbId: 8gh DbLabel: GreenFILE An: 192431918 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A robust maximum likelihood estimation approach for Ordinary Kriging with outlier-contaminated spatial data. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Yildirim%2C+Vural%22">Yildirim, Vural</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> vurall_yildirim@hotmail.com</i><br /><searchLink fieldCode="AR" term="%22Todini%2C+Ezio%22">Todini, Ezio</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> presidente-onorario@sii-ihs.it</i><br /><searchLink fieldCode="AR" term="%22Kantar%2C+Yeliz+Mert%22">Kantar, Yeliz Mert</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> ymert@eskisehir.edu.tr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Environmental+%26+Ecological+Statistics%22">Environmental & Ecological Statistics</searchLink>. Mar2026, Vol. 33 Issue 1, p513-544. 32p. – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Kriging%22">Kriging</searchLink><br /><searchLink fieldCode="DE" term="%22Robust+statistics%22">Robust statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Variograms%22">Variograms</searchLink><br /><searchLink fieldCode="DE" term="%22Outliers+%28Statistics%29%22">Outliers (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Maximum+likelihood+statistics%22">Maximum likelihood statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Spatial+data+structures%22">Spatial data structures</searchLink><br /><searchLink fieldCode="DE" term="%22Geographic+spatial+analysis%22">Geographic spatial analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Ordinary Kriging is a popular geostatistical technique for spatial interpolation and prediction. However, classical maximum likelihood estimation (MLE) of variogram parameters is known to be sensitive to outliers, resulting in biased variogram models and poor prediction performance. This study proposes a more robust MLE framework that reduces the influence of outliers while retaining the essential spatial dependence structure. Expanding on Todini and Ferraresi (1996) formulation of Kriging, robust statistical methods are incorporated into the estimation procedure, allowing for stable inference in the presence of outlier-contaminated spatial data. The proposed approach is analytically developed, and its properties are investigated using extensive Monte Carlo simulations. The practical relevance of this method is demonstrated by applying it to a real-world nitrogen dioxide (NO2) dataset. Conventional methods such as MLE, least squares, and weighted least squares estimation do not adequately capture spatial variation due to outliers. The results show that the proposed robust method improves parameter estimates and makes more reliable predictions, especially in scenarios with outlier-contaminated spatial data. These findings emphasize the importance of robust inference for Kriging's environmental applications. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Environmental & Ecological Statistics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10651-026-00706-9 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 32 StartPage: 513 Subjects: – SubjectFull: Kriging Type: general – SubjectFull: Robust statistics Type: general – SubjectFull: Variograms Type: general – SubjectFull: Outliers (Statistics) Type: general – SubjectFull: Maximum likelihood statistics Type: general – SubjectFull: Spatial data structures Type: general – SubjectFull: Geographic spatial analysis Type: general – SubjectFull: Monte Carlo method Type: general Titles: – TitleFull: A robust maximum likelihood estimation approach for Ordinary Kriging with outlier-contaminated spatial data. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Yildirim, Vural – PersonEntity: Name: NameFull: Todini, Ezio – PersonEntity: Name: NameFull: Kantar, Yeliz Mert IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 13528505 Numbering: – Type: volume Value: 33 – Type: issue Value: 1 Titles: – TitleFull: Environmental & Ecological Statistics Type: main |
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