{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,19]],"date-time":"2026-10-19T23:45:41Z","timestamp":1792453541362,"version":"4.5.0"},"reference-count":28,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2004,12,13]],"date-time":"2004-12-13T00:00:00Z","timestamp":1102896000000},"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":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["DFG Mu1230\/8-1"],"award-info":[{"award-number":["DFG Mu1230\/8-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2005,2,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We consider the problem of estimating the noise variance in homoscedastic nonparametric regression models. For low dimensional covariates t \u2208 \u211dd, d=1, 2, difference-based estimators have been investigated in a series of papers. For a given length of such an estimator, difference schemes which minimize the asymptotic mean-squared error can be computed for d=1 and d=2. However, from numerical studies it is known that for finite sample sizes the performance of these estimators may be deficient owing to a large finite sample bias. We provide theoretical support for these findings. In particular, we show that with increasing dimension d this becomes more drastic. If d\u2a7e4, these estimators even fail to be consistent. A different class of estimators is discussed which allow better control of the bias and remain consistent when d\u2a7e4. These estimators are compared numerically with kernel-type estimators (which are asymptotically efficient), and some guidance is given about when their use becomes necessary.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2005.00486.x","type":"journal-article","created":{"date-parts":[[2004,12,28]],"date-time":"2004-12-28T19:41:38Z","timestamp":1104262898000},"page":"19-41","source":"Crossref","is-referenced-by-count":63,"title":["On Difference-Based Variance Estimation in Nonparametric Regression When the Covariate is High Dimensional"],"prefix":"10.1093","volume":"67","author":[{"given":"Axel","family":"Munk","sequence":"first","affiliation":[{"name":"Georg-August-Universit\u00e4t G\u00f6ttingen , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicolai","family":"Bissantz","sequence":"additional","affiliation":[{"name":"Georg-August-Universit\u00e4t G\u00f6ttingen , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thorsten","family":"Wagner","sequence":"additional","affiliation":[{"name":"Georg-August-Universit\u00e4t G\u00f6ttingen , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gudrun","family":"Freitag","sequence":"additional","affiliation":[{"name":"Georg-August-Universit\u00e4t G\u00f6ttingen , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2004,12,13]]},"reference":[{"key":"2023040707281200800_","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1046\/j.1365-8711.2002.05720.x","article-title":"A graphical selection method for parametric models in noisy inhomogeneous regression","volume":"336","author":"Bissantz","year":"2002","journal-title":"Mnthly Notes R. 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