Influence Ranking for Multivariate Functional Data Based on Tilting

• Activity Number: 674
• Type: Topic Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yuan Yan* and Marc Georges Genton
• Companies: King Abdullah University of Science and Technology and King Abdullah University of Science and Technology
• Keywords: Data weights ; Depth ; Functional data ; Outlier ; Robustness

Abstract

Nowadays, functional data are observed more and more frequently in practice. We generalize the notion of influence ranking by tilting to multivariate functional data, where for each curve and at each time point, a vector valued observation is recorded. The tilting method ranks each curve in terms of its influence on a general statistic. This approach is based on "tilt" or reweighting each data to achieve a given small change of the statistic, while minimize the total amount of tilt. Then the influence ranking for each data corresponds to the ranking of changes in data weights. We can obtain a "center-outward" ordering for multivariate functional observations by the influence ranking with respect to functional mean, and this allows for robust analysis and outlier detection for multivariate functional data. We also propose a fast computation method for this approach. By means of a simulation study and real data examples, we compare the new approach of ordering multivariate functional data with other competitive methods based on depth.