{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,31]],"date-time":"2026-10-31T14:28:29Z","timestamp":1793456909300,"version":"4.5.0"},"reference-count":34,"publisher":"SAGE Publications","issue":"12","license":[{"start":{"date-parts":[[2020,7,19]],"date-time":"2020-07-19T00:00:00Z","timestamp":1595116800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Stat Methods Med Res"],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:p> Quantile regression is widely used to estimate conditional quantiles of an outcome variable of interest given covariates. This method can estimate one quantile at a time without imposing any constraints on the quantile process other than the linear combination of covariates and parameters specified by the regression model. While this is a flexible modeling tool, it generally yields erratic estimates of conditional quantiles and regression coefficients. Recently, parametric models for the regression coefficients have been proposed that can help balance bias and sampling variability. So far, however, only models that are linear in the parameters and covariates have been explored. This paper presents the general case of nonlinear parametric quantile models. These can be nonlinear with respect to the parameters, the covariates, or both. Some important features and asymptotic properties of the proposed estimator are described, and its finite-sample behavior is assessed in a simulation study. Nonlinear parametric quantile models are applied to estimate extreme quantiles of longitudinal measures of respiratory mechanics in asthmatic children from an epidemiological study and to evaluate a dose\u2013response relationship in a toxicological laboratory experiment. <\/jats:p>","DOI":"10.1177\/0962280220941159","type":"journal-article","created":{"date-parts":[[2020,7,20]],"date-time":"2020-07-20T04:36:28Z","timestamp":1595219788000},"page":"3757-3769","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["Nonlinear parametric quantile models"],"prefix":"10.1177","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3531-2739","authenticated-orcid":false,"given":"Matteo","family":"Bottai","sequence":"first","affiliation":[{"name":"Division of Biostatistics, Institute of Environmental Medicine, Karolinska Institutet, Stockholm, Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4305-3981","authenticated-orcid":false,"given":"Giovanna","family":"Cilluffo","sequence":"additional","affiliation":[{"name":"Institute for Biomedical Research and Innovation (IRIB), National Research Council (CNR), Palermo, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2020,7,19]]},"reference":[{"key":"bibr1-0962280220941159","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511754098"},{"key":"bibr2-0962280220941159","volume-title":"Handbook of quantile regression","author":"Koenker R","year":"2018"},{"key":"bibr3-0962280220941159","doi-asserted-by":"publisher","DOI":"10.1159\/000327206"},{"key":"bibr4-0962280220941159","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0063366"},{"key":"bibr5-0962280220941159","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2271"},{"key":"bibr6-0962280220941159","doi-asserted-by":"publisher","DOI":"10.1111\/biom.12410"},{"key":"bibr7-0962280220941159","doi-asserted-by":"publisher","DOI":"10.1080\/02664769723927"},{"key":"bibr8-0962280220941159","doi-asserted-by":"publisher","DOI":"10.1016\/j.taap.2012.01.022"},{"key":"bibr9-0962280220941159","doi-asserted-by":"publisher","DOI":"10.1021\/acs.est.7b02963"},{"key":"bibr10-0962280220941159","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780140911"},{"key":"bibr11-0962280220941159","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1999.10473882"},{"key":"bibr12-0962280220941159","volume-title":"Nonlinear regression with R","author":"Ritz C","year":"2008"},{"key":"bibr13-0962280220941159","doi-asserted-by":"publisher","DOI":"10.1006\/jmps.1999.1276"},{"key":"bibr14-0962280220941159","volume-title":"Model selection and multimodel inference: a practical information\u2013theoretical approach","author":"Burnham KP","year":"2002","edition":"2"},{"key":"bibr15-0962280220941159","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2013.836975"},{"key":"bibr16-0962280220941159","doi-asserted-by":"publisher","DOI":"10.1145\/6187.6192"},{"key":"bibr17-0962280220941159","volume-title":"Numerical methods for unconstrained optimization and nonlinear equations","author":"Dennis JE","year":"1983"},{"key":"bibr18-0962280220941159","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2007.00593.x"},{"key":"bibr19-0962280220941159","unstructured":"Chambers JM, Hastie TJ. 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