J. Nembé

How far can symmetry help? Phase transitions and symmetry selection in sparse functional data analysis

In sparse functional data analysis, where $n$ curves are each observed at $m$ random points, the covariance surface undergoes a sharp phase transition: if the covariance has smoothness $\beta$, the risk drops from the two-dimensional nonparametric rate to the parametric rate $n^{-1}$ once $m$ exceeds $m^*_n \asymp n^{1...