Title: On the functional Mahalanobis distance
Authors: Beatriz Bueno-Larraz - Universidad Autonoma de Madrid (Spain) [presenting]
Jose Berrendero - Universidad Autonoma de Madrid (Spain)
Antonio Cuevas - Autonomous University of Madrid (Spain)
Abstract: The theory of Reproducing Kernel Hilbert Spaces (RKHS's) has found many interesting applications in different fields, including statistic. For instance, it helps to partially overcome some difficulties that arise when moving from the multivariate context to the functional one, like the non-invertivility of the covariance operators. One of the problems derived from this non-invertivility is that it does not exist a functional counterpart of the Mahalanobis distance (a relevant notion of multivariate depth). We suggest a suitable functional version of this distance based on the RKHS associated with the underlying stochastic process of the data. This new statistical distance inherits some interesting properties of the original multivariate distance and has shown good performances in different problems (like functional classification, outlier detection, etc).