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In practice, however, such assumptions are hardly valid or difficult to verify. In this paper, we propose a new and flexible method for estimating the underlying covariance structure. Our proposed method does not require the covariance to be stationary or follow a parametric form. It can accommodate nonparametric space\u2010time\u2013varying mean structure of the observed data. Under some mild regularity conditions, it is shown that our estimated covariance structure converges to the true covariance structure. The proposed method is also justified numerically by a simulation study and an application to a hand, foot, and mouth disease data.<\/jats:p>","DOI":"10.1002\/sim.8315","type":"journal-article","created":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T01:54:27Z","timestamp":1562896467000},"page":"4555-4565","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Nonparametric estimation of the spatio\u2010temporal covariance structure"],"prefix":"10.1002","volume":"38","author":[{"given":"Kai","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Biostatistics University of Florida  Gainesville Florida"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4439-9466","authenticated-orcid":false,"given":"Peihua","family":"Qiu","sequence":"additional","affiliation":[{"name":"Department of Biostatistics University of Florida  Gainesville Florida"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2019,7,11]]},"reference":[{"key":"e_1_2_9_2_1","volume-title":"Statistics for Spatio\u2010Temporal Data","author":"Cressie N","year":"2011"},{"key":"e_1_2_9_3_1","volume-title":"Statistical Analysis of Spatial and Spatio\u2010Temporal Point Patterns","author":"Diggle PJ","year":"2014"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1201\/9781420072884-c23"},{"key":"e_1_2_9_5_1","volume-title":"Statistical Methods for Spatial Data Analysis","author":"Schabenberger O","year":"2005"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.7622"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s13253-013-0152-z"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1999.10473885"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/env.854"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214502760047113"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/env.1130"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/biom.12656"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02571-0_15"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1034276620"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/ast051"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176325774"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(88)90223-6"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1137\/1114019"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1990.10474936"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1009213287"},{"key":"e_1_2_9_21_1","first-page":"1955","article-title":"Kernel regression in the presence of correlated errors","volume":"12","author":"Brabanter KD","year":"2011","journal-title":"J Mach Learn Res"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.8315","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/sim.8315","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.8315","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,9]],"date-time":"2023-09-09T22:22:30Z","timestamp":1694298150000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.8315"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,11]]},"references-count":20,"journal-issue":{"issue":"23","published-print":{"date-parts":[[2019,10,15]]}},"alternative-id":["10.1002\/sim.8315"],"URL":"https:\/\/doi.org\/10.1002\/sim.8315","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,11]]},"assertion":[{"value":"2018-09-19","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-06-14","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-07-11","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}