Logarithmic energy distances and Gini covariance for Hilbert-valued random elements

Norbert Henze, M. Dolores Jiménez-Gamero

For $\alpha \in (0,2)$, the generalized energy distance and the Gini covariance statistic are based on kernels of the form $(x,y)\mapsto \Vert x-y{\Vert }^{\alpha }$, where $\Vert \cdot \Vert$ denotes the norm in…