Salvato in:
| Autori principali: | , , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2510.21277 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917039523758080 |
|---|---|
| author | Gossard, Florian Bachoc, François Baccou, Jean Gouic, Thibaut Le Liandrat, Jacques Glantz, Tony |
| author_facet | Gossard, Florian Bachoc, François Baccou, Jean Gouic, Thibaut Le Liandrat, Jacques Glantz, Tony |
| contents | This work addresses the interpolation of probability measures within a spatial statistics framework. We develop a Kriging approach in the Wasserstein space, leveraging the quantile function representation of the one-dimensional Wasserstein distance. To mitigate the inaccuracies in semivariogram estimation that arise from sparse datasets, we combine this formulation with cross-validation techniques. In particular, we introduce a variant of the virtual cross-validation formulas tailored to quantile functions. The effectiveness of the proposed method is demonstrated on a controlled toy problem as well as on a real-world application from nuclear safety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kriging measure-valued data with sparse observations: application to nuclear safety studies Gossard, Florian Bachoc, François Baccou, Jean Gouic, Thibaut Le Liandrat, Jacques Glantz, Tony Statistics Theory This work addresses the interpolation of probability measures within a spatial statistics framework. We develop a Kriging approach in the Wasserstein space, leveraging the quantile function representation of the one-dimensional Wasserstein distance. To mitigate the inaccuracies in semivariogram estimation that arise from sparse datasets, we combine this formulation with cross-validation techniques. In particular, we introduce a variant of the virtual cross-validation formulas tailored to quantile functions. The effectiveness of the proposed method is demonstrated on a controlled toy problem as well as on a real-world application from nuclear safety. |
| title | Kriging measure-valued data with sparse observations: application to nuclear safety studies |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2510.21277 |