{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T01:40:40Z","timestamp":1782870040507,"version":"3.54.5"},"reference-count":26,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T00:00:00Z","timestamp":1580083200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,4,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We propose a simple, unified, Monte-Carlo-assisted approach (called \u2018Sumca\u2019) to second-order unbiased estimation of the mean-squared prediction error (MSPE) of a small area predictor. The MSPE estimator proposed is easy to derive, has a simple expression and applies to a broad range of predictors that include the traditional empirical best linear unbiased predictor, empirical best predictor and post-model-selection empirical best linear unbiased predictor and empirical best predictor as special cases. Furthermore, the leading term of the MSPE estimator proposed is guaranteed positive; the lower order term corresponds to a bias correction, which can be evaluated via a Monte Carlo method. The computational burden for the Monte Carlo evaluation is much less, compared with other Monte-Carlo-based methods that have been used for producing second-order unbiased MSPE estimators, such as the double bootstrap and Monte Carlo jackknife. The Sumca estimator also has a nice stability feature. Theoretical and empirical results demonstrate properties and advantages of the Sumca estimator.<\/jats:p>","DOI":"10.1111\/rssb.12358","type":"journal-article","created":{"date-parts":[[2020,1,28]],"date-time":"2020-01-28T05:45:31Z","timestamp":1580190331000},"page":"467-485","source":"Crossref","is-referenced-by-count":15,"title":["Sumca: Simple, Unified, Monte-Carlo-assisted Approach to Second-Order Unbiased Mean-Squared Prediction Error Estimation"],"prefix":"10.1093","volume":"82","author":[{"given":"Jiming","family":"Jiang","sequence":"first","affiliation":[{"name":"University of California , Davis , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mahmoud","family":"Torabi","sequence":"additional","affiliation":[{"name":"University of Manitoba , Winnipeg , Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,1,27]]},"reference":[{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"818","DOI":"10.1214\/009053604000000201","article-title":"Mean squared error of empirical predictor","volume":"32","author":"Das","year":"2004","journal-title":"Ann. Statist."},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1198\/jasa.2011.tm10036","article-title":"Model selection by testing for the presence of small-area effects, and applications to area-level data","volume":"106","author":"Datta","year":"2011","journal-title":"J. Am. Statist. Ass."},{"key":"2023022408363246800_","first-page":"613","article-title":"A unified measure of uncertainty of estimated best linear unbiased predictors in small area estimation problems","volume":"10","author":"Datta","year":"2000","journal-title":"Statist. Sin."},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1093\/biomet\/92.1.183","article-title":"On measuring the variability of small area estimators under a basic area level model","volume":"92","author":"Datta","year":"2005","journal-title":"Biometrika"},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1080\/01621459.1979.10482505","article-title":"Estimates of income for small places: an application of James-Stein procedures to census data","volume":"74","author":"Fay","year":"1979","journal-title":"J. Am. Statist. Ass."},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"1733","DOI":"10.1214\/009053606000000579","article-title":"Nonparametric estimation of mean-squared prediction error in nested-error regression models","volume":"34","author":"Hall","year":"2006","journal-title":"Ann. Statist."},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1111\/j.1467-9868.2006.00541.x","article-title":"On parametric bootstrap methods for small area prediction","volume":"68","author":"Hall","year":"2006","journal-title":"J. R. Statist. Soc."},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/S0167-7152(01)00080-3","article-title":"Mixed effects models with random cluster sizes","volume":"53","author":"Jiang","year":"2001","journal-title":"Statist. Probab. Lett."},{"key":"2023022408363246800_","volume-title":"Linear and Generalized Linear Mixed Models and Their Applications","author":"Jiang","year":"2007"},{"key":"2023022408363246800_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-6827-2","volume-title":"Large Sample Techniques for Statistics","author":"Jiang","year":"2010"},{"key":"2023022408363246800_","doi-asserted-by":"crossref","DOI":"10.1201\/9781315119281","volume-title":"Asymptotic Analysis of Mixed Effects Models: Theory, Applications, and Open Problems","author":"Jiang","year":"2017"},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1023\/A:1012410420337","article-title":"Empirical best prediction for small area inference with binary data","volume":"53","author":"Jiang","year":"2001","journal-title":"Ann. Inst. Statist. Math."},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"405","DOI":"10.4310\/AMSA.2018.v3.n2.a2","article-title":"A unified Monte-Carlo jackknife for small area estimation after model selection","volume":"3","author":"Jiang","year":"2018","journal-title":"Ann. Math. Sci. Appl."},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"1782","DOI":"10.1214\/aos\/1043351257","article-title":"A unified jackknife theory for empirical best prediction with M-estimation","volume":"30","author":"Jiang","year":"2002","journal-title":"Ann. Statist."},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1080\/01621459.2014.948545","article-title":"The E-MS algorithm: model selection with incomplete data","volume":"110","author":"Jiang","year":"2015","journal-title":"J. Am. Statist. Ass."},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"1669","DOI":"10.1214\/07-AOS517","article-title":"Fence methods for mixed model selection","volume":"36","author":"Jiang","year":"2008","journal-title":"Ann. Statist."},{"key":"2023022408363246800_","volume-title":"Sumca: simple, unified, Monte-Carlo assisted approach to second-order unbiased MSPE estimation","author":"Jiang","year":"2019"},{"key":"2023022408363246800_","volume-title":"Assessing uncertainty involving model misspecification: a one-bring-one route","author":"Liu","year":"2019"},{"key":"2023022408363246800_","first-page":"1","article-title":"Small area estimation under a Fay-Herriot model with preliminary testing for the presence of random effects","volume":"41","author":"Molina","year":"2015","journal-title":"Surv. Methodol."},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1214\/12-STS410","article-title":"Model selection in linear mixed models","volume":"28","author":"M\u00fcller","year":"2013","journal-title":"Statist. Sci."},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1214\/12-STS395","article-title":"New important developments in small area estimation","volume":"28","author":"Pfeffermann","year":"2013","journal-title":"Statist. Sci."},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1080\/01621459.1990.10475320","article-title":"The estimation of mean squared errors of small area estimators","volume":"85","author":"Prasad","year":"1990","journal-title":"J. Am. Statist. Ass."},{"key":"2023022408363246800_","doi-asserted-by":"crossref","DOI":"10.1002\/9781118735855","volume-title":"Small Area Estimation","author":"Rao","year":"2015"},{"key":"2023022408363246800_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0795-5","volume-title":"The Jackknife and Bootstrap","author":"Shao","year":"1995"},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1111\/j.1467-9868.2006.00542.x","article-title":"Mean-squared error estimation in transformed Fay\u2013Herriot models","volume":"68","author":"Slud","year":"2006","journal-title":"J. R. Statist. Soc."},{"key":"2023022408363246800_","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression shrinkage and selection via the lasso","volume":"58","author":"Tibshirani","year":"1996","journal-title":"J. R. Statist. Soc."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Frssb.12358","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/82\/2\/467\/49320987\/jrsssb_82_2_467.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/82\/2\/467\/49320987\/jrsssb_82_2_467.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T19:41:56Z","timestamp":1722368516000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/82\/2\/467\/7056045"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,27]]},"references-count":26,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,1,27]]},"published-print":{"date-parts":[[2020,4,1]]}},"URL":"https:\/\/doi.org\/10.1111\/rssb.12358","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,4]]},"published":{"date-parts":[[2020,1,27]]}}}