Behavior of elemental sets in regression

David J. Olive, Douglas M. Hawkins

Research output: Contribution to journalArticle

4 Scopus citations


Elemental sets are used to produce trial estimates b of the regression coefficients β . If b0 minimizes ∥ b - β ∥ among all elemental fits b, then ∥ b0 - β ∥ = OP (n- 1), regardless of the criterion used. For any estimator bA, ∥ bA - β ∥ is at best OP (n- 1 / 2) . Hence restricting fits to elemental introduces asymptotically negligible error.

Original languageEnglish (US)
Pages (from-to)621-624
Number of pages4
JournalStatistics and Probability Letters
Issue number6
StatePublished - Mar 15 2007


  • Breakdown
  • Depth
  • LMS
  • LTA
  • Outliers
  • Robust regression

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