{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,3]],"date-time":"2024-06-03T21:14:47Z","timestamp":1717449287243},"reference-count":31,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,12,10]],"date-time":"2012-12-10T00:00:00Z","timestamp":1355097600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biometrical J"],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>In this paper, we introduce a new estimator of a percentile residual life function with censored data under a monotonicity constraint. Specifically, it is assumed that the percentile residual life is a decreasing function. This assumption is useful when estimating the percentile residual life of units, which degenerate with age. We establish a law of the iterated logarithm for the proposed estimator, and its <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/bimj1370-math-0001.png\" xlink:title=\"urn:x-wiley:03233847:bimj1370:equation:bimj1370-math-0001\" \/>\u2010equivalence to the unrestricted estimator. The asymptotic normal distribution of the estimator and its strong approximation to a Gaussian process are also established. We investigate the finite sample performance of the monotone estimator in an extensive simulation study. Finally, data from a clinical trial in primary biliary cirrhosis of the liver are analyzed with the proposed methods. One of the conclusions of our work is that the restricted estimator may be much more efficient than the unrestricted one.<\/jats:p>","DOI":"10.1002\/bimj.201100199","type":"journal-article","created":{"date-parts":[[2012,12,10]],"date-time":"2012-12-10T09:40:03Z","timestamp":1355132403000},"page":"52-67","source":"Crossref","is-referenced-by-count":8,"title":["Estimation of a monotone percentile residual life function under random censorship"],"prefix":"10.1002","volume":"55","author":[{"given":"Alba M.","family":"Franco\u2010Pereira","sequence":"first","affiliation":[{"name":"Department of Statistics and OR, Facultad de CCEE y Empresariales Universidad de Vigo, Lagoas\u2010Marcosende  36310 Vigo (Pontevedra) Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jacobo","family":"de U\u00f1a\u2010\u00c1lvarez","sequence":"additional","affiliation":[{"name":"Department of Statistics and OR, Facultad de CCEE y Empresariales Universidad de Vigo, Lagoas\u2010Marcosende  36310 Vigo (Pontevedra) Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2012,12,10]]},"reference":[{"key":"e_1_2_9_2_1","first-page":"1032","article-title":"Bootstrapping the Kaplan\u2010Meier estimator","volume":"81","author":"Akritas M.","year":"1996","journal-title":"Journal of the American Statistical Association"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0378-3758(93)90111-I"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1080\/10485259208832543"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.31.2.391"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02482529"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(89)90079-1"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.35.4.598"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-46893-3_2"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/0378-3758(92)90159-P"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970319"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610929108830485"},{"key":"e_1_2_9_13_1","volume-title":"Counting Processes and Survival Analysis","author":"Fleming T. 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