{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T17:50:55Z","timestamp":1770486655811,"version":"3.49.0"},"reference-count":32,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2014,4,8]],"date-time":"2014-04-08T00:00:00Z","timestamp":1396915200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,1,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We consider heteroscedastic regression models where the mean function is a partially linear single-index model and the variance function depends on a generalized partially linear single-index model. We do not insist that the variance function depends only on the mean function, as happens in the classical generalized partially linear single-index model. We develop efficient and practical estimation methods for the variance function and for the mean function. Asymptotic theory for the parametric and non-parametric parts of the model is developed. Simulations illustrate the results. An empirical example involving ozone levels is used to illustrate the results further and is shown to be a case where the variance function does not depend on the mean function.<\/jats:p>","DOI":"10.1111\/rssb.12066","type":"journal-article","created":{"date-parts":[[2014,4,8]],"date-time":"2014-04-08T19:52:50Z","timestamp":1396986770000},"page":"171-194","source":"Crossref","is-referenced-by-count":27,"title":["Variance Function Partially Linear Single-Index Models"],"prefix":"10.1093","volume":"77","author":[{"given":"Heng","family":"Lian","sequence":"first","affiliation":[{"name":"Nanyang Technological University , Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hua","family":"Liang","sequence":"additional","affiliation":[{"name":"George Washington University , Washington DC, , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raymond J.","family":"Carroll","sequence":"additional","affiliation":[{"name":"Texas A&M University , College Station , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2014,4,8]]},"reference":[{"key":"2023022002093729700_rssb12066-cit-0001","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1214\/aos\/1176344124","article-title":"Using residuals robustly, I: tests for heteroscedasticity, nonlinearity","volume":"6","author":"Bickel","year":"1978","journal-title":"Ann. 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