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Among the existing methods, the least squares estimator in Tong and Wang (2005) is shown to have nice statistical properties and is also easy to implement. Nevertheless, their method only applies to regression models with homoscedastic errors. In this paper, we propose two least squares estimators for the error variance in heteroscedastic nonparametric regression: the intercept estimator and the slope estimator. Both estimators are shown to be consistent and their asymptotic properties are investigated. Finally, we demonstrate through simulation studies that the proposed estimators perform better than the existing competitor in various settings.<\/jats:p>","DOI":"10.1155\/2014\/585146","type":"journal-article","created":{"date-parts":[[2014,7,3]],"date-time":"2014-07-03T21:08:02Z","timestamp":1404421682000},"page":"1-14","source":"Crossref","is-referenced-by-count":0,"title":["A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression"],"prefix":"10.1155","volume":"2014","author":[{"given":"Yuejin","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Science, Anhui University of Science and Technology, Huainan 232001, China"},{"name":"School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 20043, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yebin","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 20043, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0947-3990","authenticated-orcid":true,"given":"Tiejun","family":"Tong","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hong Kong Baptist University, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"5","first-page":"273","volume-title":"The effects of variance function estimation on prediction and calibration: an example","volume":"2","year":"1986"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-2873-3"},{"key":"14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1007\/3-540-19036-8_59","volume-title":"On the choice of the regularisation parameter in image restoration","volume":"301","year":"1988"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/75.2.189"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1990.10476211"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1991.10475090"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(97)00044-4"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1081\/STA-120006074"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346788"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/73.3.625"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/77.3.521"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00152"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1080\/0233188031000078051"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1080\/03610920802162656"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1080\/10485250802626873"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1214\/11-EJS621"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1214\/009053607000000145"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1214\/009053607000000901"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1214\/07-AOS509"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/92.4.821"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.3150\/12-BEJ432"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2012.02.050"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2006.05.015"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/585146.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/585146.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/585146.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,12]],"date-time":"2020-05-12T01:47:18Z","timestamp":1589248038000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/585146\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":23,"alternative-id":["585146","585146"],"URL":"https:\/\/doi.org\/10.1155\/2014\/585146","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}