Estimating residual variance in nonparametric regression using least squares

Tiejun Tong*, Yuedong Wang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

43 Citations (Scopus)


We propose a new estimator for the error variance in a nonparametric regression model. We estimate the error variance as the intercept in a simple linear regression model with squared differences of paired observations as the dependent variable and squared distances between the paired covariates as the regressor. For the special case of a one-dimensional domain with equally spaced design points, we show that our method reaches an asymptotic optimal rate which is not achieved by some existing methods. We conduct extensive simulations to evaluate finite-sample performance of our method and compare it with existing methods. Our method can be extended to nonparametric regression models with multivariate functions defined on arbitrary subsets of normed spaces, possibly observed on unequally spaced or clustered designed points.
Original languageEnglish
Pages (from-to)821–830
Number of pages10
Issue number4
Publication statusPublished - 1 Dec 2005

User-Defined Keywords

  • Bandwidth
  • Difference-based estimator
  • Least squares
  • Nonparametric regression
  • Quadratic form
  • Residual variance


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