On the choice of difference sequence in a unified framework for variance estimation in nonparametric regression

Wenlin Dai, Tiejun TONG*, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

7 Citations (Scopus)


Difference-based methods do not require estimating the mean function in nonparametric regression and are therefore popular in practice. In this paper, we propose a unified framework for variance estimation that combines the linear regression method with the higher-order difference estimators systematically. The unified framework has greatly enriched the existing literature on variance estimation that includes most existing estimators as special cases. More importantly, the unified framework has also provided a smart way to solve the challenging difference sequence selection problem that remains a long-standing controversial issue in nonparametric regression for several decades. Using both theory and simulations, we recommend to use the ordinary difference sequence in the unified framework, no matter if the sample size is small or if the signal-to-noise ratio is large. Finally, to cater for the demands of the application, we have developed a unified R package, named VarED, that integrates the existing difference-based estimators and the unified estimators in nonparametric regression and have made it freely available in the R statistical program http://cran.r-project.org/web/packages/.

Original languageEnglish
Pages (from-to)455-468
Number of pages14
JournalStatistical Science
Issue number3
Publication statusPublished - 2017

Scopus Subject Areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Difference-based estimator
  • Nonparametric regression
  • Optimal difference sequence
  • Ordinary difference sequence
  • Residual variance


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