Testing Outliers in Multivariate Data

  • M. L. Tiku
  • M. Singh
Part of the NATO Advanced study Institutes Series book series (ASIC, volume 79)


Given n random observations on a p-dimensional random vector x, the problem is to test whether a specified number (usually~small) of suspected observations are outliers (too discordant as compared to the bulk of observations). As a generalization of Tiku’s (1975, 1977) univariate statistic, we propose a statistic g for testing a specified number of outliers in multivariate data; g is the ratio of the product of robust estimators (Tiku, 1980) to the product of ordinary estimators of the scale parameters. For the multivariate normal, g is shown to be considerably more powerful than the prominent statistic R (restricted to the multivariate normal) due to Wilks (1963) under location shifts (model A; Barnett and Lewis, 1978) although slightly less powerful under scale changes (model B; Barnett and Lewis). Like R, g is not sensitive to changes in correlations (orientation). The statistic g can be used (under models A or B) for testing outliers in samples from any multivariate distribution whose marginal distributions are of the type (l/σ)f((x-μ)/σ).

Key Words

Multivariate outliers censored samples robust estimators modified maximum likelihood estimators 


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Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • M. L. Tiku
    • 1
  • M. Singh
    • 1
  1. 1.Department of Mathematical SciencesMcMaster UniversityHamiltonCanada

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