Relative errors of difference-based variance estimators in nonparametric regression

Tiejun Tong*, Anna Liu, Yuedong Wang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

6 Citations (Scopus)


Difference-based estimators for the error variance are popular since they do not require the estimation of the mean function. Unlike most existing difference-based estimators, new estimators proposed by Müller et al. (2003) and Tong and Wang (2005) achieved the asymptotic optimal rate as residual-based estimators. In this article, we study the relative errors of these difference-based estimators which lead to better understanding of the differences between them and residual-based estimators. To compute the relative error of the covariate-matched U-statistic estimator proposed by Müller et al. (2003), we develop a modified version by using simpler weights. We further investigate its asymptotic property for both equidistant and random designs and show that our modified estimator is asymptotically efficient.
Original languageEnglish
Pages (from-to)2890-2902
Number of pages13
JournalCommunications in Statistics - Theory and Methods
Issue number18
Publication statusPublished - Jan 2008

User-Defined Keywords

  • Asymptotically efficient
  • Bandwidth
  • Kernel estimator
  • Mean squared error
  • Nonparametric regression
  • Variance estimation


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