Breakdown points of t-type regression estimators

Xuming He, Douglas G. Simpson, Guangyu Wang

Research output: Contribution to journalArticlepeer-review

Abstract

To bound the influence of a leverage point, generalised M-estimators have been suggested. However, the usual generalised M-estimator of regression has a breakdown point that is less than the inverse of its dimension. This paper shows that dimension-independent positive breakdown points can be attained by a class of well-defined generalised M-estimators with redescending scores. The solution can be determined through optimisation of t-type likelihood applied to properly weighted residuals. The highest breakdown point of 1/2 is attained by Cauchy score. These bounded-influence and high-breakdown estimators can be viewed as a fully iterated version of the one-step generalised M-estimates of Simpson, Ruppert & Carroll (1992) with the two advantages of easier interpretability and avoidance of undesirable roots to estimating equations. Given the design-dependent weights, they can be computed via EM algorithms. Empirical investigations show that they are highly competitive with other robust estimators of regression.

Original languageEnglish (US)
Pages (from-to)675-687
Number of pages13
JournalBiometrika
Volume87
Issue number3
DOIs
StatePublished - 2000

Keywords

  • Breakdown point
  • Generalised M-estimator
  • Likelihood
  • Linear regression
  • Robustness
  • t distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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