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 language | English |
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Pages (from-to) | 1267-1276 |
Number of pages | 10 |
Journal | Linear Algebra and Its Applications |
Volume | 435 |
Issue number | 6 |
DOIs | |
Publication status | Published - 15 Sep 2011 |
Keywords
- Hat matrix
- Lagrange
- Linear regression
- Multivariate outlier