{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T16:47:39Z","timestamp":1778604459717,"version":"3.51.4"},"reference-count":31,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2020,1,29]],"date-time":"2020-01-29T00:00:00Z","timestamp":1580256000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,6,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>A two-stage normal hierarchical model called the Fay\u2013Herriot model and the empirical Bayes estimator are widely used to obtain indirect and model-based estimates of means in small areas. However, the performance of the empirical Bayes estimator can be poor when the assumed normal distribution is misspecified. This article presents a simple modification that makes use of density power divergence and proposes a new robust empirical Bayes small area estimator. The mean squared error and estimated mean squared error of the proposed estimator are derived based on the asymptotic properties of the robust estimator of the model parameters. We investigate the numerical performance of the proposed method through simulations and an application to survey data.<\/jats:p>","DOI":"10.1093\/biomet\/asz075","type":"journal-article","created":{"date-parts":[[2019,11,15]],"date-time":"2019-11-15T12:10:45Z","timestamp":1573819845000},"page":"467-480","source":"Crossref","is-referenced-by-count":13,"title":["Robust empirical Bayes small area estimation with density power divergence"],"prefix":"10.1093","volume":"107","author":[{"given":"S","family":"Sugasawa","sequence":"first","affiliation":[{"name":"Center for Spatial Information Science, The University of Tokyo, Kashiwa, Chiba 272-8568, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,1,29]]},"reference":[{"key":"2020071623112386900_B1","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/s00180-011-0301-1","article-title":"A weighted strategy to handle likelihood uncertainty in Bayesian inference","volume":"28","author":"Agostinelli,","year":"2013","journal-title":"Comp. 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