Optimal variance estimation without estimating the mean function

Tiejun TONG, Yanyuan Ma, Yuedong Wang

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

We study the least squares estimator in the residual variance estimation context. We show that the mean squared differences of paired observations are asymptotically normally distributed. We further establish that, by regressing the mean squared differences of these paired observations on the squared distances between paired covariates via a simple least squares procedure, the resulting variance estimator is not only asymptotically normal and root-n consistent, but also reaches the optimal bound in terms of estimation variance. We also demonstrate the advantage of the least squares estimator in comparison with existing methods in terms of the second order asymptotic properties.

Original languageEnglish
Pages (from-to)1839-1854
Number of pages16
JournalBernoulli
Volume19
Issue number5 A
DOIs
Publication statusPublished - 2013

Scopus Subject Areas

  • Statistics and Probability

User-Defined Keywords

  • Asymptotic normality
  • Difference-based estimator
  • Generalized least squares
  • Nonparametric regression
  • Optimal bound
  • Residual variance

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