COMPSTAT 2016: Start Registration
View Submission - CRoNoS FDA 2016
A0162
Title: Global and local functional depths Authors:  Carlo Sguera - Universidad Carlos III de Madrid (Spain) [presenting]
Pedro Galeano - Universidad Carlos III de Madrid (Spain)
Rosa Lillo - Universidad Carlos III de Madrid (Spain)
Abstract: A functional data depth provides a center-outward ordering criterion which allows robust measures, such as the median, trimmed means, central regions or ranks, to be defined in the functional framework. A functional data depth can be global or local. With global depths, the degree of centrality of a curve $x$ depends equally on the rest of the sample observations, while with local depths, the contribution of each observation in defining the degree of centrality of $x$ decreases as the distance from $x$ increases. We present a comparative analysis of the global and local approaches to the functional depth problem focusing on the ``global'' functional spatial depth (FSD) and its local version, the kernelized functional spatial depth (KFSD). First, we consider two illustrative real applications to show that FSD and KFSD may behave differently. Then, we present the results of a simulation study designed to understand when different behaviors between global and local depths should be expected.