{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T03:11:34Z","timestamp":1776136294720,"version":"3.50.1"},"reference-count":34,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T00:00:00Z","timestamp":1697673600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006093","name":"Patient-Centered Outcomes Research Institute","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006093","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,5,13]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Likelihood-based inference under nonconvex constraints on model parameters has become increasingly common in biomedical research. In this paper, we establish large-sample properties of the maximum likelihood estimator when the true parameter value lies at the boundary of a nonconvex parameter space. We further derive the asymptotic distribution of the likelihood ratio test statistic under nonconvex constraints on model parameters. A general Monte Carlo procedure for generating the limiting distribution is provided. The theoretical results are demonstrated by five examples in Anderson\u2019s stereotype logistic regression model, genetic association studies, gene-environment interaction tests, cost-constrained linear regression and fairness-constrained linear regression.<\/jats:p>","DOI":"10.1093\/biomet\/asad062","type":"journal-article","created":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T16:59:34Z","timestamp":1697734774000},"page":"591-607","source":"Crossref","is-referenced-by-count":1,"title":["Likelihood-based inference under nonconvex boundary constraints"],"prefix":"10.1093","volume":"111","author":[{"given":"J Y","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Industrial Systems Engineering & Management, National University of Singapore , Engineering Drive 2 , 117576 Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Z S","family":"Ye","sequence":"additional","affiliation":[{"name":"Department of Industrial Systems Engineering & Management, National University of Singapore , Engineering Drive 2 , 117576 Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0835-0788","authenticated-orcid":false,"given":"Y","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Epidemiology and Informatics, University of Pennsylvania , 423 Guardian Drive , Philadelphia, Pennsylvania 19104, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2023,10,19]]},"reference":[{"key":"2024051307572917200_asad062-B1","doi-asserted-by":"crossref","first-page":"3139","DOI":"10.1002\/sim.3693","article-title":"Bayesian inference for the stereotype regression model: application to a case\u2013control study of prostate cancer","volume":"28","author":"Ahn","year":"2009","journal-title":"Statist. 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