{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T14:15:41Z","timestamp":1784643341175,"version":"3.55.0"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2020,4,11]],"date-time":"2020-04-11T00:00:00Z","timestamp":1586563200000},"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\/501100003329","name":"Spanish Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100008530","name":"European Regional Development Fund","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Belgian Fund for Scientific Research"},{"name":"Louvain School of Statistics"},{"name":"Biomedical Research Centre at Vigo University"}],"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>Cross-sectional sampling is often used when investigating inter-event times, resulting in left-truncated and right-censored data. In this paper, we consider a semiparametric truncation model in which the truncating variable is assumed to belong to a certain parametric family. We examine two methods of estimating both the truncation and the lifetime distributions. We obtain asymptotic representations of the estimators for the lifetime distribution and establish their weak convergence. Both of the proposed estimators perform better than Wang\u2019s (1991) nonparametric maximum likelihood estimator in terms of the integrated mean squared error, when the parametric family for the truncation is sufficiently close to its true distribution. The full likelihood approach is preferable to the conditional likelihood approach in estimating the lifetime distribution, though not necessarily the truncation distribution. In an application to Alzheimer\u2019s disease data, hypothesis tests reject the uniform truncation distribution, but several other parametric models lead to similar behaviour of the truncation and lifetime distributions after disease onset.<\/jats:p>","DOI":"10.1093\/biomet\/asaa002","type":"journal-article","created":{"date-parts":[[2020,1,23]],"date-time":"2020-01-23T20:09:57Z","timestamp":1579810197000},"page":"449-465","source":"Crossref","is-referenced-by-count":4,"title":["Estimation from cross-sectional data under a semiparametric truncation model"],"prefix":"10.1093","volume":"107","author":[{"given":"C","family":"Heuchenne","sequence":"first","affiliation":[{"name":"HEC Management School, University of Li\u00e8ge, rue Louvrex 14, 4000 Li\u00e8ge, Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J","family":"De U\u00f1a-\u00c1lvarez","sequence":"first","affiliation":[{"name":"Department of Statistics and Operations Research, University of Vigo, 36310 Vigo, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"G","family":"Laurent","sequence":"first","affiliation":[{"name":"HEC Management School, University of Li\u00e8ge, rue Louvrex 14, 4000 Li\u00e8ge, Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,4,11]]},"reference":[{"key":"2020052509094805100_B1","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1137\/S0040585X97986783","article-title":"On the singularities of the information matrix and multipath change-point problems","volume":"58","author":"Asgharian,","year":"2014","journal-title":"Theory Prob. Appl."},{"key":"2020052509094805100_B2","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1198\/016214502753479347","article-title":"Length-biased sampling with right-censoring: An unconditional approach","volume":"97","author":"Asgharian,","year":"2002","journal-title":"J. Am. Statist. Assoc."},{"key":"2020052509094805100_B3","doi-asserted-by":"crossref","first-page":"2109","DOI":"10.1214\/009053605000000372","article-title":"Asymptotic behavior of the unconditional NPMLE of the length-biased survivor function from right censored prevalent cohort data","volume":"33","author":"Asgharian,","year":"2005","journal-title":"Ann. Statist."},{"key":"2020052509094805100_B4","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1111\/j.1467-9469.2007.00590.x","article-title":"Estimation strategies for censored lifetimes with a Lexis-diagram type model","volume":"35","author":"Brunel,","year":"2008","journal-title":"Scand. J. Statist."},{"key":"2020052509094805100_B5","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1007\/BF02506482","article-title":"Nonparametric estimation under length-biased sampling and Type I censoring: A moment based approach","volume":"56","author":"de U\u00f1a-\u00c1lvarez,","year":"2004","journal-title":"Ann. Inst. Statist. Math."},{"key":"2020052509094805100_B6","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1007\/s11146-007-9102-2","article-title":"Nonparametric estimation of households\u2019 duration of residence from panel data","volume":"39","author":"de U\u00f1a-\u00c1lvarez,","year":"2009","journal-title":"J. Real Estate Finan. Econ."},{"key":"2020052509094805100_B7","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1006\/jmva.1993.1080","article-title":"Strong representation of the survival function estimator for truncated and censored data with applications","volume":"47","author":"Gijbels,","year":"1993","journal-title":"J. Mult. Anal."},{"key":"2020052509094805100_B8","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1093\/biomet\/86.1.27","article-title":"Maximum likelihood estimation in semiparametric selection bias models with application to AIDS vaccine trials","volume":"86","author":"Gilbert,","year":"1999","journal-title":"Biometrika"},{"key":"2020052509094805100_B9","first-page":"91","article-title":"Estimation from a length-biased distribution","volume":"3","author":"Horv\u00e1th,","year":"1985","journal-title":"Statist. Decis."},{"key":"2020052509094805100_B10","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1093\/biomet\/asq069","article-title":"Nonparametric estimation for length-biased and right-censored data","volume":"98","author":"Huang,","year":"2011","journal-title":"Biometrika"},{"key":"2020052509094805100_B11","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1007\/BF01000216","article-title":"The product-limit estimator and the bootstrap: Some asymptotic representations","volume":"71","author":"Lo,","year":"1986","journal-title":"Prob. Theory Rel. Fields"},{"key":"2020052509094805100_B12","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1093\/biomet\/asp064","article-title":"Nonparametric estimation for right-censored length-biased data: A pseudo-partial likelihood approach","volume":"96","author":"Luo,","year":"2009","journal-title":"Biometrika"},{"key":"2020052509094805100_B13","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1214\/074921707000000175","article-title":"Nonparametric estimation of a distribution function under biased sampling and censoring","volume-title":"Complex Datasets and Inverse Problems: Tomography, Networks and Beyond","author":"Mandel,","year":"2007"},{"key":"2020052509094805100_B14","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1111\/j.1541-0420.2006.00710.x","article-title":"Testing goodness of fit of a uniform truncation model","volume":"63","author":"Mandel,","year":"2007","journal-title":"Biometrics"},{"key":"2020052509094805100_B15","doi-asserted-by":"crossref","first-page":"3344","DOI":"10.1016\/j.csda.2009.02.009","article-title":"Non-parametric $k$-sample tests: Density functions vs distribution functions","volume":"53","author":"Mart\u00ednez-Camblor,","year":"2009","journal-title":"Comp. Statist. Data Anal."},{"key":"2020052509094805100_B16","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.1007\/s00180-014-0496-z","article-title":"Goodness-of-fit tests for a semiparametric model under random double truncation","volume":"29","author":"Moreira,","year":"2014","journal-title":"Comp. Statist."},{"key":"2020052509094805100_B17","doi-asserted-by":"crossref","first-page":"263","DOI":"10.2307\/1403046","article-title":"Two-sample tests of Cram\u00e9r\u2013von Mises and Kolmogorov\u2013Smirnov-type for randomly censored data","volume":"52","author":"Schumacher,","year":"1984","journal-title":"Int. Statist. Rev."},{"key":"2020052509094805100_B18","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1080\/10485250701395786","article-title":"A general semiparametric model for left-truncated and right-censored data","volume":"19","author":"Shen,","year":"2007","journal-title":"J. Nonparam. Statist."},{"key":"2020052509094805100_B19","doi-asserted-by":"crossref","first-page":"4417","DOI":"10.1016\/j.csda.2009.06.013","article-title":"Semiparametric analysis of survival data with left truncation and right censoring","volume":"53","author":"Shen,","year":"2009","journal-title":"Comp. Statist. Data Anal."},{"key":"2020052509094805100_B20","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1001\/jama.1997.03540340040030","article-title":"Predicting time to nursing home care and death in individuals with Alzheimer disease","volume":"277","author":"Stern,","year":"1997","journal-title":"J. Am. Med. Assoc."},{"key":"2020052509094805100_B21","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1093\/biomet\/74.4.883","article-title":"A note on the product-limit estimator under right censoring and left truncation","volume":"74","author":"Tsai,","year":"1987","journal-title":"Biometrika"},{"key":"2020052509094805100_B22","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1080\/01621459.1989.10478828","article-title":"A semiparametric model for randomly truncated data","volume":"84","author":"Wang,","year":"1989","journal-title":"J. Am. Statist. Assoc."},{"key":"2020052509094805100_B23","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1080\/01621459.1991.10475011","article-title":"Nonparametric estimation from cross-sectional survival data","volume":"86","author":"Wang,","year":"1991","journal-title":"J. Am. Statist. Assoc."}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/107\/2\/449\/33293360\/asaa002.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/107\/2\/449\/33293360\/asaa002.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,25]],"date-time":"2020-05-25T13:10:03Z","timestamp":1590412203000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/107\/2\/449\/5819203"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,11]]},"references-count":23,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,4,11]]},"published-print":{"date-parts":[[2020,6,1]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asaa002","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,6]]},"published":{"date-parts":[[2020,4,11]]}}}