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B1478
Title: Global depths for irregularly observed multivariate functional data Authors:  Wenlin Dai - Renmin University of China (China) [presenting]
Zhuo Qu - KAUST (Saudi Arabia)
Marc Genton - KAUST (Saudi Arabia)
Abstract: Two frameworks for multivariate functional depth based on multivariate depths are introduced. The first framework is multivariate functional integrated depth, whereas the second framework, multivariate functional extremal depth, is extended from the extremal depth for univariate functional data. In each framework, global and local multivariate functional depths are proposed. Properties of population multivariate functional depths and the consistency of the finite sample depths to their population versions are proved. In addition, the estimation of finite sample depths under irregularly observed time grids is investigated. Finally, the simplified sparse functional boxplot and the simplified intensity sparse functional boxplot are proposed for visualization without the need for data reconstruction. A simulation study demonstrates the advantages of global multivariate functional depths over local multivariate functional depths in outlier detection and faster running time. An application to cyclone track data demonstrates the excellent performance of our global multivariate functional depths.