{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T15:14:01Z","timestamp":1790781241738,"version":"4.1.0"},"reference-count":54,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T00:00:00Z","timestamp":1675987200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"crossref","award":["SES-1758808"],"award-info":[{"award-number":["SES-1758808"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Progetto di Ricerca di Ateneo","award":["PRA2018-9"],"award-info":[{"award-number":["PRA2018-9"]}]},{"name":"InGRID-2 Integrating Research Infrastructure for European","award":["730998"],"award-info":[{"award-number":["730998"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,5,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we propose a flexible nested error regression small area model with high-dimensional parameter that incorporates heterogeneity in regression coefficients and variance components. We develop a new robust small area-specific estimating equations method that allows appropriate pooling of a large number of areas in estimating small area-specific model parameters. We propose a parametric bootstrap and jackknife method to estimate not only the mean squared errors but also other commonly used uncertainty measures such as standard errors and coefficients of variation. We conduct both model-based and design-based simulation experiments and real-life data analysis to evaluate the proposed methodology.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkac010","type":"journal-article","created":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T04:04:59Z","timestamp":1676001899000},"page":"212-239","source":"Crossref","is-referenced-by-count":13,"title":["A nested error regression model with high-dimensional parameter for small area estimation"],"prefix":"10.1093","volume":"85","author":[{"given":"Partha","family":"Lahiri","sequence":"first","affiliation":[{"name":"Joint Program in Survey Methodology & Department of Mathematics, University of Maryland , College Park , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4160-9387","authenticated-orcid":false,"given":"Nicola","family":"Salvati","sequence":"additional","affiliation":[{"name":"Dipartimento di Economia e Management, Universit\u00e0 di Pisa , Pisa , Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,2,10]]},"reference":[{"issue":"440","key":"2023050420355633200_qkac010-B1","doi-asserted-by":"crossref","first-page":"1555","DOI":"10.1080\/01621459.1997.10473677","article-title":"Empirical Bayes estimation of finite population means from complex survey","volume":"92","author":"Arora","year":"1997","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2023050420355633200_qkac010-B2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v067.i01","article-title":"Fitting linear mixed-effects models using lme4","volume":"67","author":"Bates","year":"2015","journal-title":"Journal of Statistical Software"},{"issue":"401","key":"2023050420355633200_qkac010-B3","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1080\/01621459.1988.10478561","article-title":"An error component model for prediction of county crop areas using survey and satellite data","volume":"83","author":"Battese","year":"1988","journal-title":"Journal of the American Statistical Association"},{"issue":"3","key":"2023050420355633200_qkac010-B4","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1111\/insr.12267","article-title":"Estimation and testing in m-quantile regression with applications to small area estimation","volume":"86","author":"Bianchi","year":"2018","journal-title":"International Statistical Review"},{"issue":"11","key":"2023050420355633200_qkac010-B5","doi-asserted-by":"crossref","first-page":"2416","DOI":"10.1080\/03610926.2013.791375","article-title":"Asymptotic properties and variance estimators of the m-quantile regression coefficients estimators","volume":"44","author":"Bianchi","year":"2015","journal-title":"Communications in Statistics \u2013 Theory and Methods"},{"issue":"4","key":"2023050420355633200_qkac010-B6","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1093\/biomet\/75.4.761","article-title":"M-quantiles","volume":"75","author":"Breckling","year":"1988","journal-title":"Biometrika"},{"key":"2023050420355633200_qkac010-B7","author":"Brown","year":"2001"},{"issue":"1","key":"2023050420355633200_qkac010-B8","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1111\/rssb.12019","article-title":"Outlier robust small area estimation","volume":"76","author":"Chambers","year":"2014","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"3","key":"2023050420355633200_qkac010-B9","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1093\/biomet\/73.3.597","article-title":"Estimating distribution functions from survey data","volume":"73","author":"Chambers","year":"1986","journal-title":"Biometrika"},{"issue":"2","key":"2023050420355633200_qkac010-B10","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1093\/biomet\/93.2.255","article-title":"M-quantile models for small area estimation","volume":"93","author":"Chambers","year":"2006","journal-title":"Biometrika"},{"issue":"10","key":"2023050420355633200_qkac010-B11","doi-asserted-by":"crossref","first-page":"2875","DOI":"10.1016\/j.csda.2012.02.006","article-title":"Small area estimation under spatial nonstationarity","volume":"56","author":"Chandra","year":"2012","journal-title":"Computational Statistics and Data Analysis"},{"issue":"2","key":"2023050420355633200_qkac010-B12","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":"The Annals of Statistics"},{"issue":"2","key":"2023050420355633200_qkac010-B13","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":"Statistica Sinica"},{"issue":"341","key":"2023050420355633200_qkac010-B205","first-page":"117","article-title":"Stein's Estimation Rule and Its Competitors--An Empirical Bayes Approach","volume":"68","author":"Efron","year":"1973","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2023050420355633200_qkac010-B14","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1002\/bimj.201200095","article-title":"Outlier robust model-assisted small area estimation","volume":"56","author":"Fabrizi","year":"2014","journal-title":"Biometrical Journal"},{"key":"2023050420355633200_qkac010-B15","first-page":"1","author":"Ghosh","year":"2020"},{"issue":"400","key":"2023050420355633200_qkac010-B16","doi-asserted-by":"crossref","first-page":"1153","DOI":"10.1080\/01621459.1987.10478553","article-title":"Robust empirical Bayes estimation of means from stratified samples","volume":"82","author":"Ghosh","year":"1987","journal-title":"Journal of the American Statistical Association"},{"key":"2023050420355633200_qkac010-B17","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-3416-1","volume-title":"Bayesian methods for finite population sampling","author":"Ghosh","year":"1997"},{"issue":"2","key":"2023050420355633200_qkac010-B18","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":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"6","key":"2023050420355633200_qkac010-B19","doi-asserted-by":"crossref","first-page":"1251","DOI":"10.2307\/1913827","article-title":"Specification tests in econometrics","volume":"46","author":"Hausman","year":"1978","journal-title":"Econometrica"},{"issue":"3","key":"2023050420355633200_qkac010-B20","doi-asserted-by":"crossref","first-page":"715","DOI":"10.2307\/2532192","article-title":"A robust approach to the analysis of repeated measures","volume":"49","author":"Higgins","year":"1993","journal-title":"Biometrics"},{"issue":"11","key":"2023050420355633200_qkac010-B21","doi-asserted-by":"crossref","first-page":"2160","DOI":"10.1080\/00949655.2012.684094","article-title":"Small area estimation under random regression coefficient models","volume":"83","author":"Hobza","year":"2013","journal-title":"Journal of Statistical Computation and Simulation"},{"key":"2023050420355633200_qkac010-B22","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-92407-6","volume-title":"A first course in Bayesian statistical methods (Vol. 580)","author":"Hoff","year":"2009"},{"key":"2023050420355633200_qkac010-B23","doi-asserted-by":"crossref","DOI":"10.1002\/0471725250","volume-title":"Robust statistics","author":"Huber","year":"1981"},{"key":"2023050420355633200_qkac010-B24","doi-asserted-by":"crossref","DOI":"10.1201\/9781315119281","volume-title":"Asymptotic analysis of mixed effects models: Theory, application, and open problems","author":"Jiang","year":"2017"},{"issue":"1","key":"2023050420355633200_qkac010-B25","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"},{"issue":"2","key":"2023050420355633200_qkac010-B26","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":"Annals of Mathematical Sciences and Applications"},{"issue":"6","key":"2023050420355633200_qkac010-B27","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":"The Annals of Statistics"},{"issue":"3","key":"2023050420355633200_qkac010-B28","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1002\/cjs.11148","article-title":"Small area estimation via heteroscedastic nested-error regression","volume":"40","author":"Jiang","year":"2012","journal-title":"Canadian Journal of Statistics"},{"issue":"494","key":"2023050420355633200_qkac010-B29","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1198\/jasa.2011.tm10221","article-title":"Best predictive small area estimation","volume":"106","author":"Jiang","year":"2011","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2023050420355633200_qkac010-B30","first-page":"37","article-title":"Observed best prediction via nested-error regression with potentially misspecified mean and variance","volume":"41","author":"Jiang","year":"2015","journal-title":"Survey Methodology"},{"key":"2023050420355633200_qkac010-B31","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511754098","volume-title":"Quantile regression","author":"Koenker","year":"2005"},{"issue":"2","key":"2023050420355633200_qkac010-B32","first-page":"465","article-title":"Prediction in heteroscedastic nested error regression models with random dispersions","volume":"26","author":"Kubokawa","year":"2016","journal-title":"Statistica Sinica"},{"issue":"2","key":"2023050420355633200_qkac010-B33","doi-asserted-by":"crossref","first-page":"624","DOI":"10.1214\/aos\/1176347130","article-title":"Assessing normality in random effects models","volume":"17","author":"Lange","year":"1989","journal-title":"The Annals of Statistics"},{"issue":"12","key":"2023050420355633200_qkac010-B34","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1641\/0006-3568(2001)051[1069:DFELAR]2.0.CO;2","article-title":"Designs for evaluating local and regional scale trends","volume":"51","author":"Larsen","year":"2001","journal-title":"Bioscience"},{"issue":"1","key":"2023050420355633200_qkac010-B35","first-page":"1","article-title":"Hierarchical Bayes modeling of survey-weighted small area proportions","volume":"40","author":"Liu","year":"2014","journal-title":"Survey Methodology"},{"issue":"540","key":"2023050420355633200_qkac010-B36","first-page":"1","article-title":"Asymptotics for EBLUPs: Nested error regression models","volume":"117","author":"Lyu","year":"2021","journal-title":"Journal of the American Statistical Association"},{"key":"2023050420355633200_qkac010-B37","first-page":"84","article-title":"Skew normal small area time models for the Brazilian annual service sector survey","volume-title":"Statistics in Transition New Series, Special Issue on Statistical Data Integration","author":"Naves","year":"2020"},{"issue":"1","key":"2023050420355633200_qkac010-B38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/1914288","article-title":"Consistent estimates based on partially consistent observations","volume":"16","author":"Neyman","year":"1948","journal-title":"Econometrica"},{"issue":"1","key":"2023050420355633200_qkac010-B39","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1111\/j.1467-9868.2007.00635.x","article-title":"Nonparametric small area estimation using penalized spline regression","volume":"70","author":"Opsomer","year":"2008","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"key":"2023050420355633200_qkac010-B40","author":"Otto","year":"1995"},{"issue":"1","key":"2023050420355633200_qkac010-B41","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":"Statistical Science"},{"issue":"409","key":"2023050420355633200_qkac010-B42","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":"Journal of the American Statistical Association"},{"key":"2023050420355633200_qkac010-B43","doi-asserted-by":"crossref","DOI":"10.1002\/9781118735855","volume-title":"Small area estimation","author":"Rao","year":"2015","edition":"2nd ed."},{"key":"2023050420355633200_qkac010-B44","volume-title":"Hierarchical linear models: Applications and data analysis methods","author":"Raudenbush","year":"2002","edition":"2nd ed."},{"issue":"4","key":"2023050420355633200_qkac010-B45","doi-asserted-by":"crossref","first-page":"1429","DOI":"10.2307\/2533273","article-title":"Robust restricted maximum likelihood in mixed linear models","volume":"51","author":"Richardson","year":"1995","journal-title":"Biometrics"},{"issue":"1","key":"2023050420355633200_qkac010-B46","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1111\/j.1467-842X.2012.00658.x","article-title":"Model-based direct estimation of small-area distributions","volume":"54","author":"Salvati","year":"2012","journal-title":"Australian and New Zealand Journal of Statistics"},{"issue":"1","key":"2023050420355633200_qkac010-B47","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1111\/rssb.12401","article-title":"Small area estimation with linked data","volume":"83","author":"Salvati","year":"2021","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"1","key":"2023050420355633200_qkac010-B48","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11749-010-0231-1","article-title":"Small area estimation via m-quantile geographically weighted regression","volume":"21","author":"Salvati","year":"2012","journal-title":"TEST"},{"issue":"3","key":"2023050420355633200_qkac010-B49","first-page":"1101","article-title":"Heteroscedastic nested error regression models with variance functions","volume":"27","author":"Sugasawa","year":"2017","journal-title":"Statistica Sinica"},{"issue":"1","key":"2023050420355633200_qkac010-B50","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1111\/sjos.12246","article-title":"Bayesian estimators for small area models shrinking both means and variances","volume":"44","author":"Sugasawa","year":"2017","journal-title":"Scandinavian Journal of Statistics"},{"issue":"2","key":"2023050420355633200_qkac010-B51","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1111\/j.1467-842X.2010.00572.x","article-title":"Robust estimation of small-area means and quantiles","volume":"52","author":"Tzavidis","year":"2010","journal-title":"Australian and New Zealand Journal of Statistics"},{"key":"2023050420355633200_qkac010-B52","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-21706-2","volume-title":"Modern applied statistics with S","author":"Venables","year":"2002"},{"issue":"1","key":"2023050420355633200_qkac010-B53","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1007\/s11749-006-0001-2","article-title":"A unified approach on residuals, leverages and outliers in the linear mixed model","volume":"16","author":"Zewotir","year":"2007","journal-title":"TEST"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/85\/2\/212\/50204577\/qkac010.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/85\/2\/212\/50204577\/qkac010.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,4]],"date-time":"2023-05-04T20:37:47Z","timestamp":1683232667000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/85\/2\/212\/7033452"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,10]]},"references-count":54,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2,10]]},"published-print":{"date-parts":[[2023,5,4]]}},"URL":"https:\/\/doi.org\/10.1093\/jrsssb\/qkac010","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,4,1]]},"published":{"date-parts":[[2023,2,10]]}}}