Title: On adaptive functional data depths
Authors: Stanislav Nagy - Charles University (Czech Republic)
Sami Helander - Aalto University School of Science (Finland) [presenting]
Germain Van Bever - Universite de Namur (Belgium)
Lauri Viitasaari - Aalto University (Finland)
Pauliina Ilmonen - Aalto University School of Science (Finland)
Abstract: Typically, in the functional context, data depth approaches heavily emphasize the location of the functions in the distribution, therefore often missing important shape or roughness features. Commonly, these depth approaches either integrate pointwise depth values to achieve a global value, or measure the expected distance from a function to the distribution. We introduce a new class of functional depths, based on the distribution of depth values along the domain, and discuss their properties. We study the asymptotic properties of these $J$th order $k$th moment integrated depths, and illustrate their usefulness in supervised functional classification. In particular, we demonstrate the importance of receptivity to shape variations, and show that, similarly to existing depth notions, the new class of depth functions takes into account the variation in location, while remaining receptive to variations in shape and roughness as well.