Depth-based inference for functional data

Robust inference tools for functional data are proposed. They are based on the notion of depth for curves. The ideas of trimmed regions, contours and central regions are extended to functions and their structural properties and asymptotic behavior are studied. Next, a scale curve is introduced to describe dispersion in a sample of functions. The computational burden of these techniques is not heavy, so they are also adequate to analyze high-dimensional data. These inferential methods are applied to several real data sets.