{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T02:56:02Z","timestamp":1774752962847,"version":"3.50.1"},"reference-count":57,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2019,1,6]],"date-time":"2019-01-06T00:00:00Z","timestamp":1546732800000},"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\/100007270","name":"University of Michigan","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007270","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006108","name":"National Center for Advancing Translational Sciences of the National Institutes of Health","doi-asserted-by":"publisher","award":["UL1TR001412"],"award-info":[{"award-number":["UL1TR001412"]}],"id":[{"id":"10.13039\/100006108","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2018T110422"],"award-info":[{"award-number":["2018T110422"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,4,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Quantile estimation has attracted significant research interest in recent years. However, there has been only a limited literature on quantile estimation in the presence of incomplete data. We propose a general framework to address this problem. Our framework combines the two widely adopted approaches for missing data analysis, the imputation approach and the inverse probability weighting approach, via the empirical likelihood method. The method proposed is capable of dealing with many different missingness settings. We mainly study three of them: estimating the marginal quantile of a response that is subject to missingness while there are fully observed covariates; estimating the conditional quantile of a fully observed response while the covariates are partially available; estimating the conditional quantile of a response that is subject to missingness with fully observed covariates and extra auxiliary variables. The method proposed allows multiple models for both the missingness probability and the data distribution. The resulting estimators are multiply robust in the sense that they are consistent if any one of these models is correctly specified. The asymptotic distributions are established by using empirical process theory.<\/jats:p>","DOI":"10.1111\/rssb.12309","type":"journal-article","created":{"date-parts":[[2019,1,7]],"date-time":"2019-01-07T04:26:01Z","timestamp":1546835161000},"page":"305-333","source":"Crossref","is-referenced-by-count":36,"title":["A General Framework for Quantile Estimation with Incomplete Data"],"prefix":"10.1093","volume":"81","author":[{"given":"Peisong","family":"Han","sequence":"first","affiliation":[{"name":"University of Michigan , Ann Arbor , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linglong","family":"Kong","sequence":"additional","affiliation":[{"name":"University of Alberta , Edmonton , Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiwei","family":"Zhao","sequence":"additional","affiliation":[{"name":"State University of New York at Buffalo \u00a0 USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingcai","family":"Zhou","sequence":"additional","affiliation":[{"name":"Nanjing Audit University \u00a0 People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2019,1,6]]},"reference":[{"key":"2023022012281408200_","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1111\/j.1541-0420.2005.00377.x","article-title":"Doubly robust estimation in missing data and causal inference models","volume":"61","author":"Bang","year":"2005","journal-title":"Biometrics"},{"key":"2023022012281408200_","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1093\/biomet\/asp033","article-title":"Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data","volume":"96","author":"Cao","year":"2009","journal-title":"Biometrika"},{"key":"2023022012281408200_","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1214\/13-STS461","article-title":"Oracle, multiple robust and multipurpose calibration in a missing response problem","volume":"29","author":"Chan","year":"2014","journal-title":"Statist. 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