dc.contributor.author Genton, Marc G. dc.contributor.author Hall, Peter dc.date.accessioned 2015-05-06T13:32:43Z dc.date.available 2015-05-06T13:32:43Z dc.date.issued 2014-12-26 dc.identifier.citation A tilting approach to ranking influence 2014:n/a Journal of the Royal Statistical Society: Series B (Statistical Methodology) dc.identifier.issn 13697412 dc.identifier.doi 10.1111/rssb.12102 dc.identifier.uri http://hdl.handle.net/10754/552392 dc.description.abstract We suggest a new approach, which is applicable for general statistics computed from random samples of univariate or vector-valued or functional data, to assessing the influence that individual data have on the value of a statistic, and to ranking the data in terms of that influence. Our method is based on, first, perturbing the value of the statistic by ‘tilting’, or reweighting, each data value, where the total amount of tilt is constrained to be the least possible, subject to achieving a given small perturbation of the statistic, and, then, taking the ranking of the influence of data values to be that which corresponds to ranking the changes in data weights. It is shown, both theoretically and numerically, that this ranking does not depend on the size of the perturbation, provided that the perturbation is sufficiently small. That simple result leads directly to an elegant geometric interpretation of the ranks; they are the ranks of the lengths of projections of the weights onto a ‘line’ determined by the first empirical principal component function in a generalized measure of covariance. To illustrate the generality of the method we introduce and explore it in the case of functional data, where (for example) it leads to generalized boxplots. The method has the advantage of providing an interpretable ranking that depends on the statistic under consideration. For example, the ranking of data, in terms of their influence on the value of a statistic, is different for a measure of location and for a measure of scale. This is as it should be; a ranking of data in terms of their influence should depend on the manner in which the data are used. Additionally, the ranking recognizes, rather than ignores, sign, and in particular can identify left- and right-hand ‘tails’ of the distribution of a random function or vector. dc.publisher Wiley dc.relation.url http://doi.wiley.com/10.1111/rssb.12102 dc.rights This is the peer reviewed version of the following article: Genton, M. G. and Hall, P. (2014), A tilting approach to ranking influence. Journal of the Royal Statistical Society: Series B (Statistical Methodology). doi: 10.1111/rssb.12102, which has been published in final form at http://doi.wiley.com/10.1111/rssb.12102. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving. dc.subject Band depth dc.subject Data weights dc.subject Functional boxplot dc.subject Functional data dc.subject Image data dc.subject Outlier dc.subject Robustness dc.title A tilting approach to ranking influence dc.type Article dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.contributor.department Spatio-Temporal Statistics and Data Analysis Group dc.contributor.department Statistics Program dc.identifier.journal Journal of the Royal Statistical Society: Series B (Statistical Methodology) dc.eprint.version Post-print dc.contributor.institution University of Melbourne; Australia dc.contributor.institution University of California at Davis, USA kaust.person Genton, Marc G. refterms.dateFOA 2015-12-26T00:00:00Z dc.date.published-online 2014-12-26 dc.date.published-print 2016-01
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