{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:52:45Z","timestamp":1760147565924,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,14]],"date-time":"2023-02-14T00:00:00Z","timestamp":1676332800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["81671633"],"award-info":[{"award-number":["81671633"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The two-sided and one-sided empirical Bayes test (EBT) rules for the parameter of a generalized exponential distribution with contaminated data (errors in variables) are constructed by a deconvolution kernel method, respectively. Under the type of the supersmooth error distributions and the supersmooth errors with the error level can be controlled situations, the asymptotically optimal uniformly over a class of prior distributions and uniform rates of convergence of the corresponding regret for the proposed EBT rules are obtained with suitable conditions. The example study shows that the assumptions and conditions of the main results of this paper are satisfied easily by calculating.<\/jats:p>","DOI":"10.3390\/sym15020511","type":"journal-article","created":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T03:09:21Z","timestamp":1676430561000},"page":"511","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Empirical Bayes Decision for a Generalized Exponential Distribution with Contaminated Data"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5902-5021","authenticated-orcid":false,"given":"Han","family":"Qiu","sequence":"first","affiliation":[{"name":"Department of Statistics, College of Science, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaqing","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Statistics, College of Science, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7213-1283","authenticated-orcid":false,"given":"Zihao","family":"Yuan","sequence":"additional","affiliation":[{"name":"Department of Statistics, College of Science, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yangxin","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Epidemiology and Biostatistics, College of Public Health, University of South Florida, Tampa, FL 33612, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.jspi.2009.07.011","article-title":"Robust empirical Bayes tests for continuous distributions","volume":"140","author":"Karunamuni","year":"2010","journal-title":"J. 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Statist."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2033","DOI":"10.1214\/22-EJS1979","article-title":"Empirical Bayes cumulative \u2113-value multiple testing procedure for sparse sequences","volume":"16","author":"Abraham","year":"2022","journal-title":"Electron. J. Stat."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"934","DOI":"10.1214\/aoms\/1177692557","article-title":"Convergence rates for empirical Bayes two-action problems II. Continuous case","volume":"43","author":"Johns","year":"1972","journal-title":"Ann. Math. Stat."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Singh, R.S., and Laisheng, W. (2000). Nonparametric empirical bayes procedures, asymptotic optimality And rates Of convergence For two-tail tests In exponential family. J. Nonparametric Stat., 475\u2013501.","DOI":"10.1080\/10485250008832819"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/S0378-3758(02)00300-2","article-title":"Rates of convergence of empirical Bayes tests for a normal mean","volume":"111","author":"Pensky","year":"2003","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.spl.2004.02.011","article-title":"On optimal convergence rate of empirical Bayes tests","volume":"68","author":"Liang","year":"2004","journal-title":"Stat. Probab. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.jspi.2004.06.036","article-title":"On empirical Bayes procedures for selecting good populations in a positive exponential family","volume":"129","author":"Gupta","year":"2005","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1184","DOI":"10.1080\/01621459.1988.10478718","article-title":"Optimal rates of convergence for deconvolving a density","volume":"83","author":"Carroll","year":"1988","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/0167-7152(90)90061-B","article-title":"Rates of convergence of some estimators in a class of deconvolution problems","volume":"9","author":"Stefanski","year":"1990","journal-title":"Stat. Probab. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1214\/aos\/1176348248","article-title":"On the optimal rates of convergence for nonparametric deconvolution problems","volume":"19","author":"Fan","year":"1991","journal-title":"Ann. Stat."},{"key":"ref_18","first-page":"541","article-title":"Global behavior of deconvolution kernel estimates","volume":"1","author":"Fan","year":"1991","journal-title":"Stat. Sin."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"155","DOI":"10.2307\/3315465","article-title":"Deconvolution with supersmooth distributions","volume":"20","author":"Fan","year":"1992","journal-title":"Can. J. Stat."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/S0378-3758(02)00108-8","article-title":"Empirical Bayes two-action problem for the continuous one-parameter exponential family with errors in variables","volume":"113","author":"Karunamuni","year":"2003","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1444","DOI":"10.1080\/03610926.2020.1764044","article-title":"Progressively Type-II censored competing risks data from the linear exponential distribution","volume":"51","author":"Davies","year":"2022","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1162","DOI":"10.1080\/03610920701713344","article-title":"Single and product moments of generalized order statistics from linear exponential distribution","volume":"37","author":"Ahmad","year":"2008","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"86","DOI":"10.2307\/2985310","article-title":"Simple mortality rates","volume":"7","author":"Broadbent","year":"1958","journal-title":"Appl. Stat."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1080\/00401706.1974.10489237","article-title":"Analysis for the linear failure-rate life-testing distribution","volume":"16","author":"Bain","year":"1974","journal-title":"Technometrics"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/511\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:34:53Z","timestamp":1760121293000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/511"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,14]]},"references-count":24,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["sym15020511"],"URL":"https:\/\/doi.org\/10.3390\/sym15020511","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,2,14]]}}}