Reducing variance in univariate smoothing

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dc.creatorCheng, Ming-Yen
dc.creatorPeng, Liang
dc.creatorWu, Jyh-Shyang
dc.date2007-08-14
dc.date.accessioned2026-07-07T08:24:36Z
dc.date.available2026-07-07T08:24:36Z
dc.descriptionA variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias remains unchanged. The nearby points are chosen to maximize the variance reduction. We study in detail the case of univariate local linear regression. While the new estimator retains many advantages of the local linear estimator, it has appealing asymptotic relative efficiencies. Bandwidth selection rules are available by a simple constant factor adjustment of those for local linear estimation. A simulation study indicates that the finite sample relative efficiency often matches the asymptotic relative efficiency for moderate sample sizes. This technique is very general and has a wide range of applications.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053606000001398 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0708.1815
dc.identifierhttp://arxiv.org/abs/0708.1815
dc.identifierAnnals of Statistics 2007, Vol. 35, No. 2, 522-542
dc.identifierdoi:10.1214/009053606000001398
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136396
dc.subjectStatistics Theory
dc.subject62G08, 62G05 (Primary); 60G20 (Secondary)
dc.titleReducing variance in univariate smoothing
dc.typetext

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