{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T03:07:11Z","timestamp":1792033631638,"version":"4.4.0"},"reference-count":26,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T00:00:00Z","timestamp":1676592000000},"content-version":"vor","delay-in-days":2549,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1406622"],"award-info":[{"award-number":["DMS-1406622"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1106518"],"award-info":[{"award-number":["DMS-1106518"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,1,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>The analysis of spatial data is based on a set of assumptions, which in practice need to be checked. A commonly used assumption is that the spatial random field is second-order stationary. In the paper, a test for spatial stationarity for irregularly sampled data is proposed. The test is based on a transformation of the data (a type of Fourier transform), where the correlations between the transformed data are close to 0 if the random field is second-order stationary. However, if the random field were second-order non-stationary, this property does not hold. Using this property a test for second-order stationarity is constructed. The test statistic is based on measuring the degree of correlation in the transformed data. The asymptotic sampling properties of the test statistic are derived under both stationarity and non-stationarity of the random field. These results motivate a graphical tool which allows a visual representation of the non-stationary features. The method is illustrated with simulations and a real data example.<\/jats:p>","DOI":"10.1111\/rssb.12161","type":"journal-article","created":{"date-parts":[[2016,2,26]],"date-time":"2016-02-26T09:06:19Z","timestamp":1456477579000},"page":"95-123","source":"Crossref","is-referenced-by-count":30,"title":["A Test for Stationarity for Irregularly Spaced Spatial Data"],"prefix":"10.1093","volume":"79","author":[{"given":"Soutir","family":"Bandyopadhyay","sequence":"first","affiliation":[{"name":"Lehigh University , Bethlehem , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Suhasini Subba","family":"Rao","sequence":"additional","affiliation":[{"name":"Texas A&M University , College Station , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2016,2,25]]},"reference":[{"key":"2023021801101844400_rssb12161-cit-0001","first-page":"221","article-title":"Asymptotic properties of discrete fourier transforms for spatial data","volume":"71","author":"Bandyopadhyay","year":"2009","journal-title":"Sankhya A"},{"key":"2023021801101844400_rssb12161-cit-0002","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1214\/14-AOS1291","article-title":"A frequency domain empirical likelihood method for irregular spaced spatial data","volume":"43","author":"Bandyopadhyay","year":"2015","journal-title":"Ann. 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