{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T17:27:08Z","timestamp":1772818028983,"version":"3.50.1"},"reference-count":25,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T00:00:00Z","timestamp":1680307200000},"content-version":"vor","delay-in-days":7487,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"US National Science Foundation","doi-asserted-by":"publisher","award":["DMS 98-16630"],"award-info":[{"award-number":["DMS 98-16630"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"US National Science Foundation","doi-asserted-by":"publisher","award":["DMS 00-72571"],"award-info":[{"award-number":["DMS 00-72571"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Statistical Research Centre for Complex Systems"},{"DOI":"10.13039\/501100002551","name":"Seoul National University, Korea","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002551","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2002,10,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Least squares methods are popular for fitting valid variogram models to spatial data. The paper proposes a new least squares method based on spatial subsampling for variogram model fitting. We show that the method proposed is statistically efficient among a class of least squares methods, including the generalized least squares method. Further, it is computationally much simpler than the generalized least squares method. The method produces valid variogram estimators under very mild regularity conditions on the underlying random field and may be applied with different choices of the generic variogram estimator without analytical calculation. An extension of the method proposed to a class of spatial regression models is illustrated with a real data example. Results from a simulation study on finite sample properties of the method are also reported.<\/jats:p>","DOI":"10.1111\/1467-9868.00364","type":"journal-article","created":{"date-parts":[[2003,3,12]],"date-time":"2003-03-12T19:37:40Z","timestamp":1047497860000},"page":"837-854","source":"Crossref","is-referenced-by-count":25,"title":["Least Squares Variogram Fitting by Spatial Subsampling"],"prefix":"10.1093","volume":"64","author":[{"given":"Yoon Dong","family":"Lee","sequence":"first","affiliation":[{"name":"Seoul National University , Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Soumendra N.","family":"Lahiri","sequence":"additional","affiliation":[{"name":"Iowa State University , Ames , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2002,10,23]]},"reference":[{"key":"2023040200505169700_","volume-title":"Preprint","author":"Barry","year":"1997"},{"key":"2023040200505169700_","doi-asserted-by":"crossref","first-page":"1921","DOI":"10.1214\/aop\/1176989004","article-title":"Equivalent mixing conditions for random fields","volume":"21","author":"Bradley","year":"1993","journal-title":"Ann. 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