Difference-based variance estimation in nonparametric regression with repeated measurement data

Wenlin Dai, Yanyuan Ma, Tiejun Tong*, Lixing Zhu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

12 Citations (Scopus)
25 Downloads (Pure)


Over the past three decades, interest in cheap yet competitive variance estimators in nonparametric regression has grown tremendously. One family of estimators which has risen to meet the task is the difference-based estimators. Unlike their residual-based counterparts, difference-based estimators do not require estimating the mean function and are therefore popular in practice. This work further develops the difference-based estimators in the repeated measurement setting for nonparametric regression models. Three difference-based methods are proposed for the variance estimation under both balanced and unbalanced repeated measurement settings: the sample variance method, the partitioning method, and the sequencing method. Both their asymptotic properties and finite sample performance are explored. The sequencing method is shown to be the most adaptive while the sample variance method and the partitioning method are shown to outperform in certain cases.

Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalJournal of Statistical Planning and Inference
Publication statusPublished - 1 Aug 2015

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

User-Defined Keywords

  • Asymptotic normality
  • Difference-based estimator
  • Least squares
  • Nonparametric regression
  • Repeated measurements
  • Residual variance


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