Representation of small ball probabilities in Hilbert space and lower bound in regression for functional data

André Mas

Let $S={\sum }_{i=1}^{+\infty }{\lambda }_i{Z}_i$ where the $Z_i$'s are i.d.d. positive with $\mathbb{E}\Vert Z{\Vert }^3<+\infty$ and $({\lambda }_i{)}_{i\in \mathbb{N}}$ a positive nonincreasing sequence…