Reducing variance in univariate smoothing

Ming-Yen Cheng, Liang Peng, Jyh-Shyang Wu

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)522-542
Number of pages21
JournalAnnals of Statistics
Volume35
Issue number2
DOIs
Publication statusPublished - Apr 2007

User-Defined Keywords

  • bandwidth
  • coverage probability
  • kernel
  • local linear regression
  • nonparametric smoothing
  • variance reduction

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