{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T18:04:50Z","timestamp":1774548290120,"version":"3.50.1"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,21]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Estimating the mean square error of a small area predictor under an informative sampling design is a challenging problem. Existing approaches rely on approximations that have not been justified theoretically. We provide rigorous support for a mean square error estimator that is applicable to an informative sample design. The procedure can be used in combination with predictors of general parameters that may be nonlinear functions of the model response variable. We also construct calibrated prediction intervals that rely less on normality than standard prediction intervals. We validate the proposed measures of uncertainty through simulation. We apply the methods to predict several functions of sheet and rill erosion for Iowa counties using data from a complex agricultural survey.<\/jats:p>","DOI":"10.1093\/biomet\/asaf065","type":"journal-article","created":{"date-parts":[[2025,9,13]],"date-time":"2025-09-13T11:45:29Z","timestamp":1757763929000},"source":"Crossref","is-referenced-by-count":0,"title":["Alternative mean square error estimators and confidence intervals for small area prediction under general designs"],"prefix":"10.1093","volume":"112","author":[{"given":"Yanghyeon","family":"Cho","sequence":"first","affiliation":[{"name":"Department of Biostatistics, Columbia University , 722 West 168th Street , New York, New York 10032, . ycho@uidaho.edu","place":["U.S.A"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emily","family":"Berg","sequence":"additional","affiliation":[{"name":"Department of Statistics, Iowa State University , 2438 Osborn Dr. , Ames, Iowa 50011,","place":["U.S.A"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,9,16]]},"reference":[{"key":"2026032613115047300_asaf065-B1","doi-asserted-by":"crossref","first-page":"673","DOI":"10.2478\/jos-2022-0031","article-title":"Construction of databases for small area estimation","volume":"38","author":"Berg","year":"2022","journal-title":"J. Offic. Statist"},{"key":"2026032613115047300_asaf065-B2","doi-asserted-by":"crossref","DOI":"10.1093\/jssam\/smae018","article-title":"Small area prediction for exponential dispersion families under informative sampling","author":"Berg","year":"2024","journal-title":"J. Survey Statist. Methodol"},{"key":"2026032613115047300_asaf065-B3","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1214\/20-AOAS1388","article-title":"An approximate best prediction approach to small area estimation for sheet and rill erosion under informative sampling","volume":"15","author":"Berg","year":"2021","journal-title":"Ann. Appl. Statist"},{"key":"2026032613115047300_asaf065-B4","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1080\/10106049.2011.562309","article-title":"Monitoring US agriculture: the US Department of Agriculture, National Agricultural Statistics Service, cropland data layer program","volume":"26","author":"Boryan","year":"2011","journal-title":"Geocarto Int"},{"key":"2026032613115047300_asaf065-B5","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/S0378-3758(02)00323-3","article-title":"On measures of uncertainty of empirical Bayes small-area estimators","volume":"112","author":"Butar","year":"2003","journal-title":"J. Statist. Plan. Infer"},{"key":"2026032613115047300_asaf065-B6","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1111\/j.2517-6161.1991.tb01817.x","article-title":"A sample reuse method for accurate parametric empirical Bayes confidence intervals","volume":"53","author":"Carlin","year":"1991","journal-title":"J. R. Statist. Soc. B"},{"key":"2026032613115047300_asaf065-B7","author":"Cho","year":"2023"},{"key":"2026032613115047300_asaf065-B8","doi-asserted-by":"crossref","first-page":"1430","DOI":"10.1093\/jssam\/smae007","article-title":"Optimal predictors of general small area parameters under an informative sample design using parametric sample distribution models","volume":"12","author":"Cho","year":"2024","journal-title":"J. Survey Statist. Methodol"},{"key":"2026032613115047300_asaf065-B9","doi-asserted-by":"crossref","first-page":"9","DOI":"10.59170\/stattrans-2016-001","article-title":"Small area prediction under alternative model specifications","volume":"17","author":"Erciulescu","year":"2016","journal-title":"Statistics in Transition new series"},{"key":"2026032613115047300_asaf065-B10","doi-asserted-by":"crossref","first-page":"2720","DOI":"10.1016\/j.csda.2006.01.012","article-title":"Estimation of the mean squared error of predictors of small area linear parameters under a logistic mixed model","volume":"51","author":"Gonz\u00e1lez-Manteiga","year":"2007","journal-title":"Comp. Statist. Data Anal"},{"key":"2026032613115047300_asaf065-B11","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1007\/s11749-018-0594-2","article-title":"A generalized mixed model for skewed distributions applied to small area estimation","volume":"28","author":"Graf","year":"2019","journal-title":"Test"},{"key":"2026032613115047300_asaf065-B12","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":"2026032613115047300_asaf065-B13","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. B"},{"key":"2026032613115047300_asaf065-B14","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1080\/00031305.1996.10473566","article-title":"Sample quantiles in statistical packages","volume":"50","author":"Hyndman","year":"1996","journal-title":"Am. Statistician"},{"key":"2026032613115047300_asaf065-B15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02595419","article-title":"Mixed model prediction and small area estimation","volume":"15","author":"Jiang","year":"2006","journal-title":"Test"},{"key":"2026032613115047300_asaf065-B16","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1093\/biomet\/asm035","article-title":"Resampling-based empirical prediction: an application to small area estimation","volume":"94","author":"Lahiri","year":"2007","journal-title":"Biometrika"},{"key":"2026032613115047300_asaf065-B17","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1093\/biomet\/asp003","article-title":"Jackknife estimation of mean squared error of small area predictors in nonlinear mixed models","volume":"96","author":"Lohr","year":"2009","journal-title":"Biometrika"},{"key":"2026032613115047300_asaf065-B18","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1002\/cjs.10051","article-title":"Small area estimation of poverty indicators","volume":"38","author":"Molina","year":"2010","journal-title":"Can. J. Statist"},{"key":"2026032613115047300_asaf065-B19","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1023\/A:1018574412308","article-title":"The national resources inventory: a long-term multi-resource monitoring programme","volume":"4","author":"Nusser","year":"1997","journal-title":"Envir. Ecol. Statist"},{"key":"2026032613115047300_asaf065-B20","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1198\/016214507000001094","article-title":"Small-area estimation under informative probability sampling of areas and within the selected areas","volume":"102","author":"Pfeffermann","year":"2007","journal-title":"J. Am. Statist. Assoc"},{"key":"2026032613115047300_asaf065-B21","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1080\/01621459.1990.10475320","article-title":"The estimation of the mean squared error of small-area estimators","volume":"85","author":"Prasad","year":"1990","journal-title":"J. Am. Statist. Assoc"},{"key":"2026032613115047300_asaf065-B22","volume-title":"R: A Language and Environment for Statistical Computing","author":"R Development Core Team","year":"2025"},{"key":"2026032613115047300_asaf065-B23","doi-asserted-by":"crossref","first-page":"1555","DOI":"10.1111\/biom.13552","article-title":"Bivariate small-area estimation for binary and Gaussian variables based on a conditionally specified model","volume":"78","author":"Sun","year":"2022","journal-title":"Biometrics"}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asaf065\/64284993\/asaf065.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/112\/4\/asaf065\/67092967\/asaf065.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/112\/4\/asaf065\/67092967\/asaf065.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T17:12:04Z","timestamp":1774545124000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/doi\/10.1093\/biomet\/asaf065\/8255758"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,10,21]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asaf065","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025]]},"published":{"date-parts":[[2025]]},"article-number":"asaf065"}}