Bounds for the largest Mahalanobis distance

Eugene G. Gath, Kevin Hayes

Research output: Contribution to journalArticlepeer-review

Abstract

Upper and lower bounds for the magnitude of the largest Mahalanobis distance, calculated from n multivariate observations of length p, are derived. These bounds are multivariate extensions of corresponding bounds that arise for the most deviant Z-score calculated from a univariate sample of size n. The approach taken is to pose optimization problems in a mathematical context and to employ variational methods to obtain solutions. The attainability of the bounds obtained is demonstrated. Bounds for related quantities (elements of the "hat matrix") are also derived.

Original languageEnglish
Pages (from-to)93-106
Number of pages14
JournalLinear Algebra and Its Applications
Volume419
Issue number1
DOIs
Publication statusPublished - 1 Nov 2006

Keywords

  • Bound
  • Inequality
  • Lagrange
  • Mahalanobis distance
  • Multivariate outlier

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