{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T21:18:31Z","timestamp":1791235111140,"version":"4.1.0"},"reference-count":43,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,4,8]],"date-time":"2023-04-08T00:00:00Z","timestamp":1680912000000},"content-version":"vor","delay-in-days":7375,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-0196041"],"award-info":[{"award-number":["DMS-0196041"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-0072400"],"award-info":[{"award-number":["DMS-0072400"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["L16385"],"award-info":[{"award-number":["L16385"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000268","name":"Biological and Biotechnology Sciences Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000268","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["96\/MMI09785"],"award-info":[{"award-number":["96\/MMI09785"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010942","name":"University of North Carolina at Charlotte","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100010942","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003,2,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Varying-coefficient linear models arise from multivariate nonparametric regression, non-linear time series modelling and forecasting, functional data analysis, longitudinal data analysis and others. It has been a common practice to assume that the varying coefficients are functions of a given variable, which is often called an index. To enlarge the modelling capacity substantially, this paper explores a class of varying-coefficient linear models in which the index is unknown and is estimated as a linear combination of regressors and\/or other variables. We search for the index such that the derived varying-coefficient model provides the least squares approximation to the underlying unknown multidimensional regression function. The search is implemented through a newly proposed hybrid backfitting algorithm. The core of the algorithm is the alternating iteration between estimating the index through a one-step scheme and estimating coefficient functions through one-dimensional local linear smoothing. The locally significant variables are selected in terms of a combined use of the t-statistic and the Akaike information criterion. We further extend the algorithm for models with two indices. Simulation shows that the methodology proposed has appreciable flexibility to model complex multivariate non-linear structure and is practically feasible with average modern computers. The methods are further illustrated through the Canadian mink\u2013muskrat data in 1925\u20131994 and the pound\u2013dollar exchange rates in 1974\u20131983.<\/jats:p>","DOI":"10.1111\/1467-9868.00372","type":"journal-article","created":{"date-parts":[[2003,3,12]],"date-time":"2003-03-12T14:37:44Z","timestamp":1047479864000},"page":"57-80","source":"Crossref","is-referenced-by-count":178,"title":["Adaptive Varying-Coefficient Linear Models"],"prefix":"10.1093","volume":"65","author":[{"given":"Jianqing","family":"Fan","sequence":"first","affiliation":[{"name":"University of North Carolina , Chapel Hill , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiwei","family":"Yao","sequence":"additional","affiliation":[{"name":"London School of Economics and Political Science , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zongwu","family":"Cai","sequence":"additional","affiliation":[{"name":"University of North Carolina , Charlotte , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2003,1,28]]},"reference":[{"key":"2023040900081488000_","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1080\/01621459.1975.10479884","article-title":"One-step Huber estimates in linear models","volume":"70","author":"Bickel","year":"1975","journal-title":"J. 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