2007/04/01 by Ming−Yen Cheng, Ming-Yen Cheng, Liang Peng +1
Mathematics · #Advanced Statistical Methods and Models #Statistical Methods and Inference #Statistical and numerical algorithms #math.ST #msc:60G20 #msc:62G05 #msc:62G08 #stat.TH
paper · pdf · doi:10.1214/009053606000001398
published as Annals of Statistics 2007, Vol. 35, No. 2, 522-542 · Published 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)
openalex publication_date 2007/04/01 · arxiv created 2007/08/14 · arxiv updated 2009/12/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28
A 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.