Bounds for a multivariate extension of range over standard deviation based on the Mahalanobis distance

E. G. Gath, K. Hayes

Research output: Contribution to journalArticlepeer-review

Abstract

The range over standard deviation of a set of univariate data points is given a natural multivariate extension through the Mahalanobis distance. The problem of finding extrema of this multivariate extension of "range over standard deviation" is investigated. The supremum (maximum) is found using Lagrangian methods and an interval is given for the infinimum. The independence of optimizing the Mahalanobis distance and the multivariate extension of range is demonstrated and connections are explored in several examples using an analogue of the "hat" matrix of linear regression.

Original languageEnglish
Pages (from-to)1267-1276
Number of pages10
JournalLinear Algebra and Its Applications
Volume435
Issue number6
DOIs
Publication statusPublished - 15 Sep 2011

Keywords

  • Hat matrix
  • Lagrange
  • Linear regression
  • Multivariate outlier

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