Simultaneous confidence bands for linear regression with heteroscedastic errors

Julian J. Faraway, Jiayang Sun

Research output: Contribution to journalArticlepeer-review


The Scheffé method may be used to construct simultaneous confidence bands for a regression surface for the whole predictor space. When the bands need only hold for a subset of that space, previous authors have described how the bands can be appropriately narrowed while still maintaining the desired level of confidence. Data with heteroscedastic errors occur often, and unless some transformation is feasible, there is no obvious way to construct bands using the current methods. This article shows how to construct approximate simultaneous confidence bands when the errors are heteroscedastic and symmetric. The method works when the weights are known or unknown and have to be estimated. The region in which the bands must hold can be quite general and will work for any linear unbiased estimate of the regression surface. The method can even be extended to linear estimates with a small amount of bias such as nonparametric kernel regression smoothers.

Original languageEnglish
Pages (from-to)1094-1098
Number of pages5
JournalJournal of the American Statistical Association
Issue number431
Publication statusPublished - 1 Jan 1995


  • Scheffé confidence interval
  • Tube formula

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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