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 language | English |
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Pages (from-to) | 93-106 |
Number of pages | 14 |
Journal | Linear Algebra and Its Applications |
Volume | 419 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Nov 2006 |
Keywords
- Bound
- Inequality
- Lagrange
- Mahalanobis distance
- Multivariate outlier