{"data":{"id":"10.6084/m9.figshare.c.2035394.v1","type":"dois","attributes":{"doi":"10.6084/m9.figshare.c.2035394.v1","prefix":"10.6084","suffix":"m9.figshare.c.2035394.v1","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Xingdong Feng","affiliation":[],"nameIdentifiers":[]},{"name":"Liping Zhu","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Estimation and Testing of Varying Coefficients in Quantile Regression"}],"publisher":"Figshare","container":{},"publicationYear":2015,"subjects":[{"subject":"Medicine"},{"subject":"Genetics"},{"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":"59999 Environmental Sciences not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Earth and related environmental sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Earth and related environmental sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"19999 Mathematical Sciences not elsewhere classified","subjectScheme":"FOR"},{"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":"Science Policy"}],"contributors":[],"dates":[{"date":"2015-12-05","dateType":"Created"},{"date":"2016-05-05","dateType":"Updated"},{"date":"2015","dateType":"Issued"}],"language":null,"types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"Collection","resourceType":"Collection","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rights":"CC-BY","rightsUri":"http://creativecommons.org/licenses/by/3.0/us"}],"descriptions":[{"description":"In this article, we establish a novel connection between the null hypothesis \u003ci\u003eH\u003c/i\u003e\u003csub\u003e0\u003c/sub\u003e on the coefficients and a rank-reducible form of the varying coefficient model in quantile regression. We use \u003ci\u003eB\u003c/i\u003e-splines to approximate the varying coefficients in the rank-reducible model, and make use of the fact that the null hypothesis \u003ci\u003eH\u003c/i\u003e\u003csub\u003e0\u003c/sub\u003e implies a unidimensional structure of a transformed coefficient matrix for the \u003ci\u003eB\u003c/i\u003e-spline basis functions. By evaluating the unidimensional structure, we alleviate the difficulty of testing such hypotheses commonly considered in varying coefficient quantile models. We demonstrate through numerical studies that the proposed method can be much more powerful than the rank score test which is widely used in the quantile regression literature. Supplementary materials for this article are available online.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"PD94bWwgdmVyc2lvbj0iMS4wIiBlbmNvZGluZz0iVVRGLTgiPz4KPHJlc291cmNlIHhtbG5zOnhzaT0iaHR0cDovL3d3dy53My5vcmcvMjAwMS9YTUxTY2hlbWEtaW5zdGFuY2UiIHhtbG5zPSJodHRwOi8vZGF0YWNpdGUub3JnL3NjaGVtYS9rZXJuZWwtNCIgeHNpOnNjaGVtYUxvY2F0aW9uPSJodHRwOi8vZGF0YWNpdGUub3JnL3NjaGVtYS9rZXJuZWwtNCBodHRwOi8vc2NoZW1hLmRhdGFjaXRlLm9yZy9tZXRhL2tlcm5lbC00L21ldGFkYXRhLnhzZCI+CiAgPGlkZW50aWZpZXIgaWRlbnRpZmllclR5cGU9IkRPSSI+MTAuNjA4NC9NOS5GSUdTSEFSRS5DLjIwMzUzOTQuVjE8L2lkZW50aWZpZXI+CiAgPGNyZWF0b3JzPgogICAgPGNyZWF0b3I+CiAgICAgIDxjcmVhdG9yTmFtZT5YaW5nZG9uZyBGZW5nPC9jcmVhdG9yTmFtZT4KICAgIDwvY3JlYXRvcj4KICAgIDxjcmVhdG9yPgogICAgICA8Y3JlYXRvck5hbWU+TGlwaW5nIFpodTwvY3JlYXRvck5hbWU+CiAgICA8L2NyZWF0b3I+CiAgPC9jcmVhdG9ycz4KICA8dGl0bGVzPgogICAgPHRpdGxlPkVzdGltYXRpb24gYW5kIFRlc3Rpbmcgb2YgVmFyeWluZyBDb2VmZmljaWVudHMgaW4gUXVhbnRpbGUgUmVncmVzc2lvbjwvdGl0bGU+CiAgPC90aXRsZXM+CiAgPHB1Ymxpc2hlcj5GaWdzaGFyZTwvcHVibGlzaGVyPgogIDxwdWJsaWNhdGlvblllYXI+MjAxNTwvcHVibGljYXRpb25ZZWFyPgogIDxyZXNvdXJjZVR5cGUgcmVzb3VyY2VUeXBlR2VuZXJhbD0iQ29sbGVjdGlvbiI+Q29sbGVjdGlvbjwvcmVzb3VyY2VUeXBlPgogIDxzdWJqZWN0cz4KICAgIDxzdWJqZWN0Pk1lZGljaW5lPC9zdWJqZWN0PgogICAgPHN1YmplY3Q+R2VuZXRpY3M8L3N1YmplY3Q+CiAgICA8c3ViamVjdCBzdWJqZWN0U2NoZW1lPSJGaWVsZHMgb2YgU2NpZW5jZSBhbmQgVGVjaG5vbG9neSAoRk9TKSIgc2NoZW1lVVJJPSJodHRwOi8vd3d3Lm9lY2Qub3JnL3NjaWVuY2UvaW5uby8zODIzNTE0Ny5wZGYiPkZPUzogQmlvbG9naWNhbCBzY2llbmNlczwvc3ViamVjdD4KICAgIDxzdWJqZWN0IHN1YmplY3RTY2hlbWU9IkZpZWxkcyBvZiBTY2llbmNlIGFuZCBUZWNobm9sb2d5IChGT1MpIj5GT1M6IEJpb2xvZ2ljYWwgc2NpZW5jZXM8L3N1YmplY3Q+CiAgICA8c3ViamVjdCBzdWJqZWN0U2NoZW1lPSJGT1IiPjU5OTk5IEVudmlyb25tZW50YWwgU2NpZW5jZXMgbm90IGVsc2V3aGVyZSBjbGFzc2lmaWVkPC9zdWJqZWN0PgogICAgPHN1YmplY3Qgc3ViamVjdFNjaGVtZT0iRmllbGRzIG9mIFNjaWVuY2UgYW5kIFRlY2hub2xvZ3kgKEZPUykiIHNjaGVtZVVSST0iaHR0cDovL3d3dy5vZWNkLm9yZy9zY2llbmNlL2lubm8vMzgyMzUxNDcucGRmIj5GT1M6IEVhcnRoIGFuZCByZWxhdGVkIGVudmlyb25tZW50YWwgc2NpZW5jZXM8L3N1YmplY3Q+CiAgICA8c3ViamVjdCBzdWJqZWN0U2NoZW1lPSJGaWVsZHMgb2YgU2NpZW5jZSBhbmQgVGVjaG5vbG9neSAoRk9TKSI+Rk9TOiBFYXJ0aCBhbmQgcmVsYXRlZCBlbnZpcm9ubWVudGFsIHNjaWVuY2VzPC9zdWJqZWN0PgogICAgPHN1YmplY3Qgc3ViamVjdFNjaGVtZT0iRk9SIj4xOTk5OSBNYXRoZW1hdGljYWwgU2NpZW5jZXMgbm90IGVsc2V3aGVyZSBjbGFzc2lmaWVkPC9zdWJqZWN0PgogICAgPHN1YmplY3Qgc3ViamVjdFNjaGVtZT0iRmllbGRzIG9mIFNjaWVuY2UgYW5kIFRlY2hub2xvZ3kgKEZPUykiIHNjaGVtZVVSST0iaHR0cDovL3d3dy5vZWNkLm9yZy9zY2llbmNlL2lubm8vMzgyMzUxNDcucGRmIj5GT1M6IE1hdGhlbWF0aWNzPC9zdWJqZWN0PgogICAgPHN1YmplY3Qgc3ViamVjdFNjaGVtZT0iRmllbGRzIG9mIFNjaWVuY2UgYW5kIFRlY2hub2xvZ3kgKEZPUykiPkZPUzogTWF0aGVtYXRpY3M8L3N1YmplY3Q+CiAgICA8c3ViamVjdD5TY2llbmNlIFBvbGljeTwvc3ViamVjdD4KICA8L3N1YmplY3RzPgogIDxkYXRlcz4KICAgIDxkYXRlIGRhdGVUeXBlPSJDcmVhdGVkIj4yMDE1LTEyLTA1PC9kYXRlPgogICAgPGRhdGUgZGF0ZVR5cGU9IlVwZGF0ZWQiPjIwMTYtMDUtMDU8L2RhdGU+CiAgICA8ZGF0ZSBkYXRlVHlwZT0iSXNzdWVkIj4yMDE1PC9kYXRlPgogIDwvZGF0ZXM+CiAgPHNpemVzLz4KICA8Zm9ybWF0cy8+CiAgPHZlcnNpb24vPgogIDxyaWdodHNMaXN0PgogICAgPHJpZ2h0cyByaWdodHNVUkk9Imh0dHA6Ly9jcmVhdGl2ZWNvbW1vbnMub3JnL2xpY2Vuc2VzL2J5LzMuMC91cyI+Q0MtQlk8L3JpZ2h0cz4KICA8L3JpZ2h0c0xpc3Q+CiAgPGRlc2NyaXB0aW9ucz4KICAgIDxkZXNjcmlwdGlvbiBkZXNjcmlwdGlvblR5cGU9IkFic3RyYWN0Ij5JbiB0aGlzIGFydGljbGUsIHdlIGVzdGFibGlzaCBhIG5vdmVsIGNvbm5lY3Rpb24gYmV0d2VlbiB0aGUgbnVsbCBoeXBvdGhlc2lzICZsdDtpJmd0O0gmbHQ7L2kmZ3Q7Jmx0O3N1YiZndDswJmx0Oy9zdWImZ3Q7IG9uIHRoZSBjb2VmZmljaWVudHMgYW5kIGEgcmFuay1yZWR1Y2libGUgZm9ybSBvZiB0aGUgdmFyeWluZyBjb2VmZmljaWVudCBtb2RlbCBpbiBxdWFudGlsZSByZWdyZXNzaW9uLiBXZSB1c2UgJmx0O2kmZ3Q7QiZsdDsvaSZndDstc3BsaW5lcyB0byBhcHByb3hpbWF0ZSB0aGUgdmFyeWluZyBjb2VmZmljaWVudHMgaW4gdGhlIHJhbmstcmVkdWNpYmxlIG1vZGVsLCBhbmQgbWFrZSB1c2Ugb2YgdGhlIGZhY3QgdGhhdCB0aGUgbnVsbCBoeXBvdGhlc2lzICZsdDtpJmd0O0gmbHQ7L2kmZ3Q7Jmx0O3N1YiZndDswJmx0Oy9zdWImZ3Q7IGltcGxpZXMgYSB1bmlkaW1lbnNpb25hbCBzdHJ1Y3R1cmUgb2YgYSB0cmFuc2Zvcm1lZCBjb2VmZmljaWVudCBtYXRyaXggZm9yIHRoZSAmbHQ7aSZndDtCJmx0Oy9pJmd0Oy1zcGxpbmUgYmFzaXMgZnVuY3Rpb25zLiBCeSBldmFsdWF0aW5nIHRoZSB1bmlkaW1lbnNpb25hbCBzdHJ1Y3R1cmUsIHdlIGFsbGV2aWF0ZSB0aGUgZGlmZmljdWx0eSBvZiB0ZXN0aW5nIHN1Y2ggaHlwb3RoZXNlcyBjb21tb25seSBjb25zaWRlcmVkIGluIHZhcnlpbmcgY29lZmZpY2llbnQgcXVhbnRpbGUgbW9kZWxzLiBXZSBkZW1vbnN0cmF0ZSB0aHJvdWdoIG51bWVyaWNhbCBzdHVkaWVzIHRoYXQgdGhlIHByb3Bvc2VkIG1ldGhvZCBjYW4gYmUgbXVjaCBtb3JlIHBvd2VyZnVsIHRoYW4gdGhlIHJhbmsgc2NvcmUgdGVzdCB3aGljaCBpcyB3aWRlbHkgdXNlZCBpbiB0aGUgcXVhbnRpbGUgcmVncmVzc2lvbiBsaXRlcmF0dXJlLiBTdXBwbGVtZW50YXJ5IG1hdGVyaWFscyBmb3IgdGhpcyBhcnRpY2xlIGFyZSBhdmFpbGFibGUgb25saW5lLjwvZGVzY3JpcHRpb24+CiAgPC9kZXNjcmlwdGlvbnM+CjwvcmVzb3VyY2U+Cg==","url":"https://figshare.com/collections/Estimation_and_Testing_of_Varying_Coefficients_in_Quantile_Regression/2035394/1","contentUrl":null,"metadataVersion":3,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","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":"2015-12-05T19:39:59.000Z","registered":"2015-12-05T19:40:00.000Z","published":"2015","updated":"2024-12-16T12:53:03.000Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}},"provider":{"data":{"id":"otjm","type":"providers"}},"media":{"data":{"id":"10.6084/m9.figshare.c.2035394.v1","type":"media"}},"references":{"data":[]},"citations":{"data":[]},"parts":{"data":[]},"partOf":{"data":[]},"versions":{"data":[]},"versionOf":{"data":[]}}}}