{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T17:15:50Z","timestamp":1792689350817,"version":"4.5.0"},"reference-count":29,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2006,3,3]],"date-time":"2006-03-03T00:00:00Z","timestamp":1141344000000},"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":[[2006,4,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>The particularly wide range of applications of small area prediction, e.g. in policy making decisions, has meant that this topic has received substantial attention in recent years. The problems of estimating mean-squared predictive error, of correcting that estimator for bias and of constructing prediction intervals have been addressed by various workers, although existing methodology is still restricted to a narrow range of models. To overcome this difficulty we develop new, bootstrap-based methods, which are applicable in very general settings, for constructing bias-corrected estimators of mean-squared error and for computing prediction regions. Unlike existing techniques, which are based largely on Taylor expansions, our bias-corrected mean-squared error estimators do not require analytical calculation. They also have the property that they are non-negative. Our prediction intervals have a high degree of coverage accuracy, O(n\u22123), where n is the number of areas, if double-bootstrap methods are employed. The techniques do not depend on the form of the small area estimator and are applicable to general two-level, small area models, where the variables at either level can be discrete or continuous and, in particular, can be non-normal. Most importantly, the new methods are simple and easy to apply.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2006.00541.x","type":"journal-article","created":{"date-parts":[[2006,3,3]],"date-time":"2006-03-03T10:10:01Z","timestamp":1141380601000},"page":"221-238","source":"Crossref","is-referenced-by-count":161,"title":["On Parametric Bootstrap Methods for Small Area Prediction"],"prefix":"10.1093","volume":"68","author":[{"given":"Peter","family":"Hall","sequence":"first","affiliation":[{"name":"Australian National University , Canberra , Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tapabrata","family":"Maiti","sequence":"additional","affiliation":[{"name":"Australian National University , Canberra , Australia"},{"name":"Iowa State University , Ames , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2006,3,3]]},"reference":[{"key":"2023040707474184700_","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/S0167-7152(03)00214-1","article-title":"On sieve bootstrap prediction intervals","volume":"65","author":"Alonso","year":"2003","journal-title":"Statist. Probab. Lett."},{"key":"2023040707474184700_","first-page":"1053","article-title":"On the superiority of the Bayesian method over the BLUP in small area estimation problems","volume":"7","author":"Arora","year":"1997","journal-title":"Statist. Sin."},{"key":"2023040707474184700_","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":"J. Am. Statist. Ass."},{"key":"2023040707474184700_","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1080\/01621459.1998.10474107","article-title":"Standard errors of prediction in generalized linear mixed models","volume":"93","author":"Booth","year":"1998","journal-title":"J. Am. Statist. Ass."},{"key":"2023040707474184700_","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: model selection, model diagnostics, empirical Bayes and hierarchical Bayes","volume":"112","author":"Butar Butar","year":"2003","journal-title":"J. Statist. Planng Inf."},{"key":"2023040707474184700_","doi-asserted-by":"crossref","first-page":"671","DOI":"10.2307\/2532003","article-title":"Empirical Bayes estimates of age standardized relative risks for use in disease mapping","volume":"43","author":"Clayton","year":"1987","journal-title":"Biometrics"},{"key":"2023040707474184700_","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1093\/oxfordjournals.aje.a116410","article-title":"Principle lifetime occupation and cognitive impairment in a French Elderly Cohort","volume":"135","author":"Dartigues","year":"1992","journal-title":"Am. J. Epidem."},{"key":"2023040707474184700_","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":"2023040707474184700_","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":"2023040707474184700_","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1080\/01621459.1979.10482505","article-title":"Estimation of income from small places: an application of James\u2013Stein procedures to census data","volume":"74","author":"Fay","year":"1979","journal-title":"J. Am. Statist. 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Forecast."},{"key":"2023040707474184700_","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/S0169-2070(03)00007-4","article-title":"Bootstrap prediction intervals for autoregression using asymptotically mean-unbiased estimators","volume":"20","author":"Kim","year":"2004","journal-title":"Int. J. Forecast."},{"key":"2023040707474184700_","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1214\/ss\/1063994975","article-title":"On the impact of bootstrap in survey sampling and small-area estimation","volume":"18","author":"Lahiri","year":"2003","journal-title":"Statist. Sci."},{"key":"2023040707474184700_","first-page":"1","article-title":"A review of empirical best linear unbiased prediction for the Fay-Herriot small-area model","volume":"52","author":"Lahiri","year":"2003","journal-title":"Philip. 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