{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T13:08:54Z","timestamp":1772284134453,"version":"3.50.1"},"reference-count":21,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,2,8]],"date-time":"2012-02-08T00:00:00Z","timestamp":1328659200000},"content-version":"vor","delay-in-days":38,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11001247"],"award-info":[{"award-number":["11001247"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["103709"],"award-info":[{"award-number":["103709"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Research Grants Council of Hong Kong","award":["11001247"],"award-info":[{"award-number":["11001247"]}]},{"name":"Research Grants Council of Hong Kong","award":["103709"],"award-info":[{"award-number":["103709"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We study learning algorithms generated by regularization schemes in reproducing\nkernel Hilbert spaces associated with an <jats:italic>\u03f5<\/jats:italic>\u2010insensitive pinball loss. This loss\nfunction is motivated by the <jats:italic>\u03f5<\/jats:italic>\u2010insensitive loss for support vector regression and the\npinball loss for quantile regression. Approximation analysis is conducted for these\nalgorithms by means of a variance\u2010expectation bound when a noise condition is\nsatisfied for the underlying probability measure. The rates are explicitly derived\nunder a priori conditions on approximation and capacity of the reproducing kernel\nHilbert space. As an application, we get approximation orders for the support\nvector regression and the quantile regularized regression.<\/jats:p>","DOI":"10.1155\/2012\/902139","type":"journal-article","created":{"date-parts":[[2012,2,8]],"date-time":"2012-02-08T21:04:03Z","timestamp":1328735043000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Approximation Analysis of Learning Algorithms for Support Vector Regression and Quantile Regression"],"prefix":"10.1155","volume":"2012","author":[{"given":"Dao-Hong","family":"Xiang","sequence":"first","affiliation":[]},{"given":"Ting","family":"Hu","sequence":"additional","affiliation":[]},{"given":"Ding-Xuan","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,2,8]]},"reference":[{"key":"e_1_2_7_1_2","series-title":"Adaptive and Learning Systems for Signal Processing, Communications, and Control","volume-title":"Statistical Learning Theory","author":"Vapnik V. 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