On Nonparametric Estimation of Covariogram
The paper overviews and investigates several nonparametric methods of estimating covariograms. It provides a unified approach and notation to compare the main approaches used in applied research. The primary focus is on methods that utilise the actual values of observations, rather than their ranks...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Austrian Statistical Society
2025-01-01
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| Series: | Austrian Journal of Statistics |
| Online Access: | https://www.ajs.or.at/index.php/ajs/article/view/1975 |
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| _version_ | 1841543719117914112 |
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| author | Adam Bilchouris Andriy Olenko |
| author_facet | Adam Bilchouris Andriy Olenko |
| author_sort | Adam Bilchouris |
| collection | DOAJ |
| description |
The paper overviews and investigates several nonparametric methods of estimating covariograms. It provides a unified approach and notation to compare the main approaches used in applied research. The primary focus is on methods that utilise the actual values of observations, rather than their ranks. We concentrate on such desirable properties of covariograms as bias, positive-definiteness and behaviour at large distances. The paper discusses several theoretical properties and demonstrates some surprising drawbacks of well-known estimators. Numerical studies provide a comparison of representatives from different methods using various metrics. The results provide important insight and guidance for practitioners who use estimated covariograms in various applications, including kriging, monitoring network optimisation, cross-validation, and other related tasks.
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| format | Article |
| id | doaj-art-ba9ec8d6437c475e876df797fb6f3e16 |
| institution | Kabale University |
| issn | 1026-597X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Austrian Statistical Society |
| record_format | Article |
| series | Austrian Journal of Statistics |
| spelling | doaj-art-ba9ec8d6437c475e876df797fb6f3e162025-01-13T07:12:21ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2025-01-0154110.17713/ajs.v54i1.1975On Nonparametric Estimation of CovariogramAdam Bilchouris0Andriy Olenko1La Trobe UniversityLa Trobe University The paper overviews and investigates several nonparametric methods of estimating covariograms. It provides a unified approach and notation to compare the main approaches used in applied research. The primary focus is on methods that utilise the actual values of observations, rather than their ranks. We concentrate on such desirable properties of covariograms as bias, positive-definiteness and behaviour at large distances. The paper discusses several theoretical properties and demonstrates some surprising drawbacks of well-known estimators. Numerical studies provide a comparison of representatives from different methods using various metrics. The results provide important insight and guidance for practitioners who use estimated covariograms in various applications, including kriging, monitoring network optimisation, cross-validation, and other related tasks. https://www.ajs.or.at/index.php/ajs/article/view/1975 |
| spellingShingle | Adam Bilchouris Andriy Olenko On Nonparametric Estimation of Covariogram Austrian Journal of Statistics |
| title | On Nonparametric Estimation of Covariogram |
| title_full | On Nonparametric Estimation of Covariogram |
| title_fullStr | On Nonparametric Estimation of Covariogram |
| title_full_unstemmed | On Nonparametric Estimation of Covariogram |
| title_short | On Nonparametric Estimation of Covariogram |
| title_sort | on nonparametric estimation of covariogram |
| url | https://www.ajs.or.at/index.php/ajs/article/view/1975 |
| work_keys_str_mv | AT adambilchouris onnonparametricestimationofcovariogram AT andriyolenko onnonparametricestimationofcovariogram |