{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T03:36:33Z","timestamp":1791171393679,"version":"4.1.0"},"reference-count":0,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[1998,9,1]],"date-time":"1998-09-01T00:00:00Z","timestamp":904608000000},"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":[[1998,9,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>It has long been recognized that the mean provides an inadequate summary whereas the set of quantiles can supply a more complete description of a sample. We introduce bivariate quantile smoothing splines, which belong to the space of bilinear tensor product splines, as nonparametric estimators for the conditional quantile functions in a two-dimensional design space. The estimators can be computed by using standard linear programming techniques and can further be used as building-blocks for conditional quantile estimations in higher dimensions. For moderately large data sets, we recommend penalized bivariate B-splines as approximate solutions. We use real and simulated data to illustrate the methodology proposed.<\/jats:p>","DOI":"10.1111\/1467-9868.00138","type":"journal-article","created":{"date-parts":[[2003,3,12]],"date-time":"2003-03-12T19:34:43Z","timestamp":1047497683000},"page":"537-550","source":"Crossref","is-referenced-by-count":76,"title":["Bivariate Quantile Smoothing Splines"],"prefix":"10.1093","volume":"60","author":[{"given":"Xuming","family":"He","sequence":"first","affiliation":[{"name":"University of Illinois , Champaign , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P.","family":"Ng","sequence":"additional","affiliation":[{"name":"University of Illinois , Champaign , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"Portnoy","sequence":"additional","affiliation":[{"name":"University of Illinois , Champaign , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2002,1,6]]},"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2F1467-9868.00138","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/60\/3\/537\/49588987\/jrsssb_60_3_537.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/60\/3\/537\/49588987\/jrsssb_60_3_537.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T05:20:12Z","timestamp":1679462412000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/60\/3\/537\/7083084"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,9,1]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2002,1,6]]},"published-print":{"date-parts":[[1998,9,1]]}},"URL":"https:\/\/doi.org\/10.1111\/1467-9868.00138","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1998,9]]},"published":{"date-parts":[[1998,9,1]]}}}