Nonparametric regression based on discretely sampled curves
  In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators based on the unobserved whole trajectories. As a consequence, we derive asymptotic results for most of the regularization techniques used in functional data analysis, including smoothing and basis representation. 
Forzani Liliana, Fraiman Ricardo and Llop Pamela
math.ST stat.TH