{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T11:13:09Z","timestamp":1791198789239,"version":"4.1.0"},"reference-count":61,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2023,3,11]],"date-time":"2023-03-11T00:00:00Z","timestamp":1678492800000},"content-version":"vor","delay-in-days":3915,"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":["0904177"],"award-info":[{"award-number":["0904177"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,11,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Modelling of spatiotemporal processes has received considerable attention in recent statistical research. However, owing to the high dimensionality of the data, the joint modelling of spatial and temporal processes presents a great computational challenge, in both likelihood-based and Bayesian approaches. We propose a joint composite estimating function approach to estimating spatiotemporal covariance structures. This substantially reduces the computational complexity and is more efficient than existing composite likelihood methods. The novelty of the proposed joint composite estimating function is rooted in the construction of three sets of estimating functions from spatial, temporal and spatiotemporal cross-pairs, which results in overidentified estimating functions. Thus, we form a joint inference function in a spirit that is similar to Hansen\u2019s generalized method of moments. We show that under practical scenarios the estimator proposed is consistent and asymptotically normal. Simulation studies prove that our method performs well in finite samples. Finally, we illustrate the joint composite estimating function method by estimating the spatiotemporal dependence structure of airborne particulates (PM10) in the north-eastern USA over a 32-month period.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2012.01035.x","type":"journal-article","created":{"date-parts":[[2012,6,21]],"date-time":"2012-06-21T19:48:24Z","timestamp":1340308104000},"page":"799-824","source":"Crossref","is-referenced-by-count":33,"title":["Joint Composite Estimating Functions in Spatiotemporal Models"],"prefix":"10.1093","volume":"74","author":[{"given":"Yun","family":"Bai","sequence":"first","affiliation":[{"name":"University of Michigan , Ann Arbor , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter X.-K.","family":"Song","sequence":"additional","affiliation":[{"name":"University of Michigan , Ann Arbor , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T. E.","family":"Raghunathan","sequence":"additional","affiliation":[{"name":"University of Michigan , Ann Arbor , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2012,6,21]]},"reference":[{"key":"2023031201055091700_","volume-title":"Handbook of Mathematical Functions","author":"Abramowitz","year":"1972"},{"key":"2023031201055091700_","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1111\/j.1467-9868.2008.00663.x","article-title":"Gaussian predictive process models for large spatial data sets","volume":"70","author":"Banerjee","year":"2008","journal-title":"J. R. Statist. Soc. B"},{"key":"2023031201055091700_","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2011.646928","article-title":"Estimating space and space-time covariance functions: a weighted composite likelihood approach","author":"Bevilacqua","year":"2011","journal-title":"J. Am. Statist. 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