Multivalued functional depth
We introduce a statistical depth function designed for highly complex functional data. These data are multivalued and observed on individual grid domains, with each observation defined over a different interval, starting and ending at different points, and recorded at unequally spaced time values that may include both dense and sparse regions. Our aim is to employ this function to identify the central element within a sample of phase portraits. To build the depth measure, we develop a dissimilarity criterion between phase portraits that incorporates their perimeter in an original way. We then apply the proposed methodology to Biomechanical data. The deepest elements obtained with our approach are compared with the mean function, which in this setting fails to reflect the actual structure of the observed sample.
Keywords: Functional data analysis statisical data depth