{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T10:01:01Z","timestamp":1770458461166,"version":"3.49.0"},"reference-count":19,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,11,25]],"date-time":"2020-11-25T00:00:00Z","timestamp":1606262400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"PUENTE","award":["UA"],"award-info":[{"award-number":["UA"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we introduce a novel parametric quantile regression model for asymmetric response variables, where the response variable follows a power skew-normal distribution. By considering a new convenient parametrization, these distribution results are very useful for modeling different quantiles of a response variable on the real line. The maximum likelihood method is employed to estimate the model parameters. Besides, we present a local influence study under different perturbation settings. Some numerical results of the estimators in finite samples are illustrated. In order to illustrate the potential for practice of our model, we apply it to a real dataset.<\/jats:p>","DOI":"10.3390\/sym12121938","type":"journal-article","created":{"date-parts":[[2020,11,25]],"date-time":"2020-11-25T21:55:06Z","timestamp":1606341306000},"page":"1938","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Parametric Quantile Regression Model for Asymmetric Response Variables on the Real Line"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8184-7403","authenticated-orcid":false,"given":"Diego I.","family":"Gallardo","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1530000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1182-5193","authenticated-orcid":false,"given":"Marcelo","family":"Bourguignon","sequence":"additional","affiliation":[{"name":"Departamento de Estat\u00edstica, Universidade Federal do Rio Grande do Norte, Natal, RN 59000-000, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4818-6006","authenticated-orcid":false,"given":"Christian E.","family":"Galarza","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Escuela Superior Polit\u00e9cnica del Litoral, ESPOL, Guayaquil 090150, Ecuador"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H\u00e9ctor W.","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,25]]},"reference":[{"key":"ref_1","first-page":"171","article-title":"A class of distributions which includes the normal ones","volume":"12","author":"Azzalini","year":"1985","journal-title":"Scand. J. Stat."},{"key":"ref_2","first-page":"199","article-title":"Further results on a class of distributions which includes the normal ones","volume":"46","author":"Azzalini","year":"1986","journal-title":"Statistica"},{"key":"ref_3","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. Stat. Theory Methods"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1007\/s11749-011-0280-0","article-title":"Likelihood-based inference for power distributions","volume":"21","author":"Pewsey","year":"2012","journal-title":"Test"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1214\/aoms\/1177729080","article-title":"The power of rank tests","volume":"24","author":"Lehmann","year":"1953","journal-title":"Ann. Math. 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Theory Methods"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s11749-014-0406-2","article-title":"Doubly censored power-normal regression models with inflation","volume":"24","author":"Bolfarine","year":"2015","journal-title":"Test"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1414","DOI":"10.1080\/02331888.2013.826659","article-title":"Skew-normal alpha-power model","volume":"48","author":"Bolfarine","year":"2014","journal-title":"Statistics"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1002\/env.2256","article-title":"The log alpha-power asymmetric distribution with application to air pollution","volume":"25","author":"Bolfarine","year":"2014","journal-title":"Environmetrics"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1002\/bimj.201100116","article-title":"Asymmetric regression models with limited responses with an application to antibody response to vaccine","volume":"55","author":"Bolfarine","year":"2013","journal-title":"Biom. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1080\/00401706.1977.10489493","article-title":"Detection of influential observation in linear regression","volume":"19","author":"Cook","year":"1977","journal-title":"Technometrics"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Cook, R.D., and Weisberg, S. (1994). An Introduction to Regression Graphics, Wiley.","DOI":"10.1002\/9780470316863"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1002\/sta4.140","article-title":"Robust quantile regression using a generalized class of skewed distributions","volume":"6","author":"Galarza","year":"2017","journal-title":"Stat"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A new look at the statistical model identification","volume":"19","author":"Akaike","year":"1974","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_18","first-page":"83","article-title":"Sulla determinazione empirica di una legge di distribuzionc","volume":"4","author":"Kolmogorov","year":"1933","journal-title":"Giorn. Ist. Ital. Attuar."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1080\/10618600.1996.10474708","article-title":"Randomized quantile residuals","volume":"5","author":"Dunn","year":"1996","journal-title":"J. Comput. Graph. 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