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Bootstrap confidence intervals for the contributions of individual variables to a Mahalanobis distance

Shabuz, Zillur R. and Garthwaite, Paul H. (2018). Bootstrap confidence intervals for the contributions of individual variables to a Mahalanobis distance. Journal of Statistical Computation and Simulation, 88(11) pp. 2232–2258.

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Hotelling's T 2 and Mahalanobis distance are widely used in the statistical analysis of multivariate data. When either of these quantities is large, a natural question is: How do individual variables contribute to its size? The Garthwaite–Koch partition has been proposed as a means of assessing the contribution of each variable. This yields point estimates of each variable's contribution and here we consider bootstrap methods for forming interval estimates of these contributions. New bootstrap methods are proposed and compared with the percentile, bias-corrected percentile, non-studentized pivotal and studentized pivotal methods via a large simulation study. The new methods enable use of a broader range of pivotal quantities than with standard pivotal methods, including vector pivotal quantities. In the context considered here, this obviates the need for transformations and leads to intervals that have higher coverage, and yet are narrower, than intervals given by the standard pivotal methods. These results held both when the population distributions were multivariate normal and when they were skew with heavy tails. Both equal-tailed intervals and shortest intervals are constructed; the latter are particularly attractive when (as here) squared quantities are of interest.

Item Type: Journal Item
Copyright Holders: 2018 Informa UK Limited, trading as Taylor & Francis Group
ISSN: 1563-5163
Keywords: Bootstrap; Garthwaite–Koch partition; Mahalanobis distance; percentile method; pivot; studentized pivotal; vector pivotal
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 54258
SWORD Depositor: Jisc Publications-Router
Depositing User: Jisc Publications-Router
Date Deposited: 11 Apr 2018 10:32
Last Modified: 29 Mar 2020 06:22
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