{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,3]],"date-time":"2026-10-03T01:33:25Z","timestamp":1790991205061,"version":"4.1.0"},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2021,10,7]],"date-time":"2021-10-07T00:00:00Z","timestamp":1633564800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"NSF\/DMS","award":["1916349"],"award-info":[{"award-number":["1916349"]}]},{"name":"NSF\/DMS","award":["2113778"],"award-info":[{"award-number":["2113778"]}]},{"name":"NSF\/DMS","award":["2113779"],"award-info":[{"award-number":["2113779"]}]},{"name":"NSF\/IIS","award":["1562303"],"award-info":[{"award-number":["1562303"]}]},{"name":"NIH\/NIEHS","award":["1R01ES027027"],"award-info":[{"award-number":["1R01ES027027"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,11,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Spatial process models popular in geostatistics often represent the observed data as the sum of a smooth underlying process and white noise. The variation in the white noise is attributed to measurement error, or microscale variability, and is called the \u2018nugget\u2019. We formally establish results on the identifiability and consistency of the nugget in spatial models based upon the Gaussian process within the framework of in-fill asymptotics, that is the sample size increases within a sampling domain that is bounded. Our work extends results in fixed domain asymptotics for spatial models without the nugget. More specifically, we establish the identifiability of parameters in the Mat\u00e9rn covariogram and the consistency of their maximum likelihood estimators in the presence of discontinuities due to the nugget. We also present simulation studies to demonstrate the role of the identifiable quantities in spatial interpolation.<\/jats:p>","DOI":"10.1111\/rssb.12472","type":"journal-article","created":{"date-parts":[[2021,10,8]],"date-time":"2021-10-08T23:29:34Z","timestamp":1633735774000},"page":"1044-1070","source":"Crossref","is-referenced-by-count":20,"title":["On Identifiability and Consistency of The Nugget in Gaussian Spatial Process Models"],"prefix":"10.1093","volume":"83","author":[{"given":"Wenpin","family":"Tang","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering and Operations Research , , New York, New York , USA"},{"name":"Columbia University , , New York, New York , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Statistics , , New York, New York , USA"},{"name":"Columbia University , , New York, New York , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sudipto","family":"Banerjee","sequence":"additional","affiliation":[{"name":"Department of Biostatistics , , Los Angeles, California , USA"},{"name":"University of California Los Angeles , , Los Angeles, California , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2021,10,7]]},"reference":[{"key":"2023022408374099100_","author":"Abramowitz","year":"1965"},{"issue":"2","key":"2023022408374099100_","doi-asserted-by":"crossref","first-page":"870","DOI":"10.1214\/09-AOS725","article-title":"On the consistent separation of scale and variance for Gaussian random fields","volume":"38","author":"Anderes","year":"2010","journal-title":"The Annals of Statistics"},{"issue":"2","key":"2023022408374099100_","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1214\/17-BA1056R","article-title":"High-dimensional Bayesian geostatistics","volume":"12","author":"Banerjee","year":"2017","journal-title":"Bayesian Analysis"},{"key":"2023022408374099100_","first-page":"1348","article-title":"Approximation beats concentration? 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