{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:35:30Z","timestamp":1760150130883,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,17]],"date-time":"2023-10-17T00:00:00Z","timestamp":1697500800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FONDECYT","award":["11190636"],"award-info":[{"award-number":["11190636"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Many phenomena can be described by random variables that follow asymmetrical distributions. In the context of regression, when the response variable Y follows such a distribution, it is preferable to estimate the response variable for predictor values using the conditional median. Quantile regression models can be employed for this purpose. However, traditional models do not incorporate a distributional assumption for the response variable. To introduce a distributional assumption while preserving model flexibility, we propose new varying-coefficients quantile regression models based on the family of log-symmetric distributions. We achieve this by reparametrizing the distribution of the response variable using quantiles. Parameter estimation is performed using a maximum likelihood penalized method, and a back-fitting algorithm is developed. Additionally, we propose diagnostic techniques to identify potentially influential local observations and leverage points. Finally, we apply and illustrate the methodology using real pollution data from Padre Las Casas city, one of the most polluted cities in Latin America and the Caribbean according to the World Air Quality Index Ranking.<\/jats:p>","DOI":"10.3390\/axioms12100976","type":"journal-article","created":{"date-parts":[[2023,10,17]],"date-time":"2023-10-17T08:25:09Z","timestamp":1697531109000},"page":"976","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Modeling Environmental Pollution Using Varying-Coefficients Quantile Regression Models under Log-Symmetric Distributions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9892-425X","authenticated-orcid":false,"given":"Luis","family":"S\u00e1nchez","sequence":"first","affiliation":[{"name":"Institute of Statistics, Universidad Austral de Chile, Valdivia 5110234, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4021-7699","authenticated-orcid":false,"given":"Germ\u00e1n","family":"Ibacache-Pulgar","sequence":"additional","affiliation":[{"name":"Institute of Statistics, Universidad de Valpara\u00edso, Valpara\u00edso 2360102, Chile"},{"name":"Centro Interdisciplinario de Estudios Atmosf\u00e9ricos y Astroestad\u00edstica, Universidad de Valpara\u00edso, Valpara\u00edso 2360102, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1832-4444","authenticated-orcid":false,"given":"Carolina","family":"Marchant","sequence":"additional","affiliation":[{"name":"Faculty of Basic Sciences, Universidad Cat\u00f3lica del Maule, Talca 3480112, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Riquelme","sequence":"additional","affiliation":[{"name":"Institute of Statistics, Universidad de Valpara\u00edso, Valpara\u00edso 2360102, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1007\/s11749-014-0401-7","article-title":"A semiparametric approach for joint modeling of median and skewness","volume":"24","author":"Vanegas","year":"2015","journal-title":"Test"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1465","DOI":"10.1081\/STA-120037254","article-title":"A New Class of Skew-Normal Distributions","volume":"33","author":"Quintana","year":"2004","journal-title":"Commun. 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