Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4603876 | Linear Algebra and its Applications | 2006 | 14 Pages |
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.
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