Constrained M-estimation for multivariate location and scatter

John T. Kent, David E. Tyler

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


Consider the problem of estimating the location vector and scatter matrix from a set of multivariate data. Two standard classes of robust estimates are M-estimates and S-estimates. The M-estimates can be tuned to give good local robustness properties, such as good efficiency and a good bound on the influence function at an underlying distribution such as the multivariate normal. However, M-estimates suffer from poor breakdown properties in high dimensions. On the other hand, S-estimates can be tuned to have good breakdown properties, but when tuned in this way, they tend to suffer from poor local robustness properties. In this paper a hybrid estimate called a constrained M-estimate is proposed which combines both good local and good global robustness properties.

Original languageEnglish (US)
Pages (from-to)1346-1370
Number of pages25
JournalAnnals of Statistics
Issue number3
StatePublished - Jun 1996

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Breakdown
  • M-estimates
  • Robustness
  • S-estimates

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