The change-of-variance function of M-estimators of scale under general contamination

Marc G. Genton, Peter J. Rousseeuw*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

In this paper we derive the change-of-variance function of M-estimators of scale under general contamination, thereby extending the formula in Hampel et al. (1986). We say that an M-estimator is B-robust if its influence function is bounded, and we call it V-robust if its change-of-variance function is bounded from above. It is shown, for a natural class of M-estimators, that the general notion of V-robustness still implies B-robustness. Several classes of M-estimators are studied closely, as well as some typical examples and their interpretation.

Original languageEnglish (US)
Pages (from-to)69-80
Number of pages12
JournalJournal of Computational and Applied Mathematics
Volume64
Issue number1-2
DOIs
StatePublished - Nov 30 1995

Keywords

  • B-robustness
  • Change-of-variance function
  • Influence function
  • V-robustness

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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