Outlier … … …. s

R. J. Beckman, R. D. Cook

Research output: Contribution to journalArticlepeer-review

311 Scopus citations


The concern over outliers is old and undoubtedly dates back to the first attempt to base conclusions on a set of statistical data. Comments by Bernoulli (1777) indicate that the practice of discarding discordant observations was commonplace 200 years ago. The history of the treatment of such observations is traced from these early comments to the present. For simple normal samples, M estimators, L estimators, and Bayesian estimators are presented as techniques that accommodate outliers in estimation. For the study of concomitant variables, methods are given for the outright rejection of discordant observations. Rejection techniques for multiple outliers are reviewed, as are the effects of masking and swamping. Methods for the detection of outliers in a regression setting are given for various models. Influence functions in multiple regression are discussed and compared with both the classical and the Bayesian methods of outlier detection. Work on outliers in circular data, discriminant analysis, experimental design, multivariate data, generalized linear models, distributions other than normal, and time series is also reviewed.

Original languageEnglish (US)
Pages (from-to)119-149
Number of pages31
Issue number2
StatePublished - May 1983


  • Bayesian outlier analysis
  • Design
  • Diagnostics
  • Discriminant analysis
  • Generalized linear models
  • Generalized residuals
  • Influential observations
  • L estimation
  • Masking
  • Multivariate outliers
  • Outher history
  • Regression
  • Residual analysis
  • Robust estimation
  • Swamping

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