Functional estimation in continuous or discretized time
Functional estimation

In many applications, observations take the form of curves, such as electricity consumption, variations in stock market prices over the course of a session, electrocardiograms...

Such phenomena can be modeled by considering families $\left(X_t,\mathrm{\hspace{0.17em}}t\in ℝ\right)$ of time-indexed random variables.

If X _t have the same distribution μ, then we can define the empirical distribution function associated with the observation of (X _t ,0 ≤ t≤T) by posing :