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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.
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]
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Database: GreenFILE
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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]
ISSN:13528505
DOI:10.1007/s10651-026-00706-9