{"data":{"id":"10.6084/m9.figshare.1202157","type":"dois","attributes":{"doi":"10.6084/m9.figshare.1202157","prefix":"10.6084","suffix":"m9.figshare.1202157","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Yoonsuh Jung","affiliation":[],"nameIdentifiers":[]},{"name":"Yoonkyung Lee","affiliation":[],"nameIdentifiers":[]},{"name":"MacEachern, Steven N.","nameType":"Personal","givenName":"Steven N.","familyName":"MacEachern","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Efficient quantile regression for heteroscedastic models"}],"publisher":"Taylor \u0026 Francis","container":{},"publicationYear":2015,"subjects":[{"subject":"Mathematics"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Mathematics","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Biological Sciences"},{"subject":"Ecology"},{"subject":"FOS: Biological sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Biological sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Earth and Environmental Sciences"},{"subject":"Biotechnology"},{"subject":"Physiology"}],"contributors":[],"dates":[{"date":"2014-10-13","dateType":"Created"},{"date":"2015-12-02","dateType":"Updated"},{"date":"2015","dateType":"Issued"}],"language":null,"types":{"ris":"DATA","bibtex":"misc","citeproc":"dataset","schemaOrg":"Dataset","resourceType":"Dataset","resourceTypeGeneral":"Dataset"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1080/00949655.2014.967244","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["438180 Bytes"],"formats":[],"version":null,"rightsList":[{"rights":"Creative Commons Attribution 4.0 International","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-4.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"Quantile regression (QR) provides estimates of a range of conditional quantiles. This stands in contrast to traditional regression techniques, which focus on a single conditional mean function. Lee et al. [Regularization of case-specific parameters for robustness and efficiency. Statist Sci. 2012;27(3):350–372] proposed efficient QR by rounding the sharp corner of the loss. The main modification generally involves an asymmetric ℓ\u003csub\u003e2\u003c/sub\u003e adjustment of the loss function around zero. We extend the idea of ℓ\u003csub\u003e2\u003c/sub\u003e adjusted QR to linear heterogeneous models. The ℓ\u003csub\u003e2\u003c/sub\u003e adjustment is constructed to diminish as sample size grows. Conditions to retain consistency properties are also provided.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://tandf.figshare.com/articles/dataset/Efficient_quantile_regression_for_heteroscedastic_models/1202157","contentUrl":null,"metadataVersion":3,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":0,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2014-10-13T10:51:16.000Z","registered":"2014-10-13T10:51:18.000Z","published":"2015","updated":"2020-09-04T21:00:16.000Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}},"provider":{"data":{"id":"otjm","type":"providers"}},"media":{"data":{"id":"10.6084/m9.figshare.1202157","type":"media"}},"references":{"data":[]},"citations":{"data":[]},"parts":{"data":[]},"partOf":{"data":[]},"versions":{"data":[]},"versionOf":{"data":[]}}}}