{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T06:52:05Z","timestamp":1791528725951,"version":"4.3.4"},"reference-count":47,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"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":[[2016,9,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution non-parametrically, given independent and identically distributed data from the mixture model, using ideas from shape-restricted function estimation. We establish the consistency of our estimators. We find the rate of convergence and asymptotic limit of the estimator for the mixing proportion. Completely automated distribution-free honest finite sample lower confidence bounds are developed for the mixing proportion. Connection to the problem of multiple testing is discussed. The identifiability of the model and the estimation of the density of the unknown distribution are also addressed. We compare the estimators proposed, which are easily implementable, with some of the existing procedures through simulation studies and analyse two data sets: one arising from an application in astronomy and the other from a microarray experiment.<\/jats:p>","DOI":"10.1111\/rssb.12148","type":"journal-article","created":{"date-parts":[[2016,1,2]],"date-time":"2016-01-02T15:23:17Z","timestamp":1451748197000},"page":"869-893","source":"Crossref","is-referenced-by-count":31,"title":["Estimation of a Two-component Mixture Model with Applications to Multiple Testing"],"prefix":"10.1093","volume":"78","author":[{"given":"Rohit Kumar","family":"Patra","sequence":"first","affiliation":[{"name":"Columbia University , New York , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bodhisattva","family":"Sen","sequence":"additional","affiliation":[{"name":"Columbia University , New York , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2016,1,1]]},"reference":[{"key":"2023021709311391600_rssb12148-cit-0001","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1214\/aoms\/1177729437","article-title":"Asymptotic theory of certain \u201cgoodness of fit\u201d criteria based on stochastic processes","volume":"23","author":"Anderson","year":"1952","journal-title":"Ann. 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