{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,30]],"date-time":"2026-05-30T00:57:56Z","timestamp":1780102676973,"version":"3.54.0"},"reference-count":29,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2013,3,20]],"date-time":"2013-03-20T00:00:00Z","timestamp":1363737600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003385","name":"University of G\u00f6ttingen","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003385","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,9,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>There are two popular smoothing parameter selection methods for spline smoothing. First, smoothing parameters can be estimated by minimizing criteria that approximate the average mean-squared error of the regression function estimator. Second, the maximum likelihood paradigm can be employed, under the assumption that the regression function is a realization of some stochastic process. The asymptotic properties of both smoothing parameter estimators for penalized splines are studied and compared. A simulation study and a real data example illustrate the theoretical findings.<\/jats:p>","DOI":"10.1111\/rssb.12010","type":"journal-article","created":{"date-parts":[[2013,3,20]],"date-time":"2013-03-20T13:18:15Z","timestamp":1363785495000},"page":"725-741","source":"Crossref","is-referenced-by-count":13,"title":["Smoothing Parameter Selection in two Frameworks for Penalized Splines"],"prefix":"10.1093","volume":"75","author":[{"given":"Tatyana","family":"Krivobokova","sequence":"first","affiliation":[{"name":"Georg-August-Universit\u00e4t G\u00f6ttingen , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2013,3,20]]},"reference":[{"key":"2023031109461042900_","volume-title":"Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables","author":"Abramowitz","year":"1972"},{"key":"2023031109461042900_","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/BF02532251","article-title":"Fitting autoregressive models for prediction","volume":"21","author":"Akaike","year":"1969","journal-title":"Ann. 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