Publicação
An approach for valid covariance estimation via the Fourier series
| Resumo: | The use of kriging for construction of prediction or risk maps requires estimating the dependence structure of the random process, which can be addressed through the approximation of the covariance function. The nonparametric estimators used for the latter aim are not necessarily valid to solve the kriging system, since the positive-definiteness condition of the covariance estimator typically fails. The usage of a parametric covariance instead may be attractive at first because of its simplicity, although it may be affected by misspecification. An alternative is suggested in this paper to obtain a valid covariance from a nonparametric estimator through the Fourier series tool, which involves two issues: estimation of the Fourier coefficients and selection of the truncation point to determine the number of terms in the Fourier expansion. Numerical studies for simulated data have been conducted to illustrate the performance of this approach. In addition, an application to a real environmental data set is included, related to the presence of nitrate in groundwater in Beja district (Portugal), so that pollution maps of the region are generated by solving the kriging equations with the use of the Fourier series estimates of the covariance. |
|---|---|
| Autores principais: | García Soidán, Pilar |
| Outros Autores: | Menezes, Raquel; Rubinos-Lopez, Oscar |
| Assunto: | Covariance function Fourier series Kriging Truncation point |
| Ano: | 2012 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso restrito |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| _version_ | 1866876551256080384 |
|---|---|
| author | García Soidán, Pilar |
| author2 | Menezes, Raquel Rubinos-Lopez, Oscar |
| author2_role | author author |
| author_facet | García Soidán, Pilar Menezes, Raquel Rubinos-Lopez, Oscar |
| author_role | author |
| contributor_name_str_mv | Universidade do Minho |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"García Soidán, Pilar\"},{\"Person.name\":\"Menezes, Raquel\"},{\"Person.name\":\"Rubinos-Lopez, Oscar\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Universidade do Minho |
| datacite.creators.creator.creatorName.fl_str_mv | García Soidán, Pilar Menezes, Raquel Rubinos-Lopez, Oscar |
| datacite.date.Accepted.fl_str_mv | 2012-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2011-07-26T16:31:21Z |
| datacite.date.embargoed.fl_str_mv | 2011-07-26T16:31:21Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_16ec |
| datacite.subjects.subject.fl_str_mv | Covariance function Fourier series Kriging Truncation point |
| datacite.titles.title.fl_str_mv | An approach for valid covariance estimation via the Fourier series |
| dc.contributor.none.fl_str_mv | Universidade do Minho |
| dc.creator.none.fl_str_mv | García Soidán, Pilar Menezes, Raquel Rubinos-Lopez, Oscar |
| dc.date.Accepted.fl_str_mv | 2012-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2011-07-26T16:31:21Z |
| dc.date.embargoed.fl_str_mv | 2011-07-26T16:31:21Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | https://hdl.handle.net/1822/13067 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Springer |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_16ec |
| dc.subject.none.fl_str_mv | Covariance function Fourier series Kriging Truncation point |
| dc.title.fl_str_mv | An approach for valid covariance estimation via the Fourier series |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | The use of kriging for construction of prediction or risk maps requires estimating the dependence structure of the random process, which can be addressed through the approximation of the covariance function. The nonparametric estimators used for the latter aim are not necessarily valid to solve the kriging system, since the positive-definiteness condition of the covariance estimator typically fails. The usage of a parametric covariance instead may be attractive at first because of its simplicity, although it may be affected by misspecification. An alternative is suggested in this paper to obtain a valid covariance from a nonparametric estimator through the Fourier series tool, which involves two issues: estimation of the Fourier coefficients and selection of the truncation point to determine the number of terms in the Fourier expansion. Numerical studies for simulated data have been conducted to illustrate the performance of this approach. In addition, an application to a real environmental data set is included, related to the presence of nitrate in groundwater in Beja district (Portugal), so that pollution maps of the region are generated by solving the kriging equations with the use of the Fourier series estimates of the covariance. |
| dirty | 0 |
| eu_rights_str_mv | restrictedAccess |
| format | article |
| fulltext.url.fl_str_mv | https://prod-dspace.uminho.pt/bitstreams/b4ca3211-4bda-4813-8ba1-4d4035a7edd0/download |
| id | rum_c0914aa4b07c37ed13f75203c00a28d2 |
| identifier.url.fl_str_mv | https://hdl.handle.net/1822/13067 |
| instacron_str | repositorium |
| institution | Universidade do Minho |
| instname_str | Universidade do Minho |
| language | eng |
| network_acronym_str | rum |
| network_name_str | RepositóriUM - Universidade do Minho |
| oai_identifier_str | oai:repositorium.uminho.pt:1822/13067 |
| organization_str_mv | urn:organizationAcronym:repositorium |
| person_str_mv | García Soidán, Pilar Menezes, Raquel Rubinos-Lopez, Oscar |
| publishDate | 2012 |
| publisher.none.fl_str_mv | Springer |
| reponame_str | RepositóriUM - Universidade do Minho |
| repository_id_str | urn:repositoryAcronym:rum |
| service_str_mv | urn:repositoryAcronym:rum |
| spelling | engSpringerporThe use of kriging for construction of prediction or risk maps requires estimating the dependence structure of the random process, which can be addressed through the approximation of the covariance function. The nonparametric estimators used for the latter aim are not necessarily valid to solve the kriging system, since the positive-definiteness condition of the covariance estimator typically fails. The usage of a parametric covariance instead may be attractive at first because of its simplicity, although it may be affected by misspecification. An alternative is suggested in this paper to obtain a valid covariance from a nonparametric estimator through the Fourier series tool, which involves two issues: estimation of the Fourier coefficients and selection of the truncation point to determine the number of terms in the Fourier expansion. Numerical studies for simulated data have been conducted to illustrate the performance of this approach. In addition, an application to a real environmental data set is included, related to the presence of nitrate in groundwater in Beja district (Portugal), so that pollution maps of the region are generated by solving the kriging equations with the use of the Fourier series estimates of the covariance.application/pdfporAn approach for valid covariance estimation via the Fourier seriesGarcía Soidán, PilarMenezes, RaquelRubinos-Lopez, OscarHostingInstitutionOrganizationalUniversidade do Minhoe-mailmailto:repositorium@usdb.uminho.ptrepositorium@usdb.uminho.ptISSNIsPartOf1866-6280ISSNIsPartOf1866-6299DOIIsPartOf10.1007/s12665-011-1269-42011-07-26T16:31:21Z20122012-01-01T00:00:00ZHandlehttps://hdl.handle.net/1822/13067http://purl.org/coar/access_right/c_16ecrestricted accessCovariance functionFourier seriesKrigingTruncation point1840257 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articlehttp://purl.org/coar/access_right/c_16ecapplication/pdffulltexthttps://prod-dspace.uminho.pt/bitstreams/b4ca3211-4bda-4813-8ba1-4d4035a7edd0/download |
| spellingShingle | An approach for valid covariance estimation via the Fourier series García Soidán, Pilar Covariance function Fourier series Kriging Truncation point |
| status | SINGLETON |
| subject.fl_str_mv | Covariance function Fourier series Kriging Truncation point |
| title | An approach for valid covariance estimation via the Fourier series |
| title_full | An approach for valid covariance estimation via the Fourier series |
| title_fullStr | An approach for valid covariance estimation via the Fourier series |
| title_full_unstemmed | An approach for valid covariance estimation via the Fourier series |
| title_short | An approach for valid covariance estimation via the Fourier series |
| title_sort | An approach for valid covariance estimation via the Fourier series |
| topic | Covariance function Fourier series Kriging Truncation point |
| topic_facet | Covariance function Fourier series Kriging Truncation point |
| url | https://hdl.handle.net/1822/13067 |
| visible | 1 |