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In this paper, we are interested in nonparametric kernel estimation of ageneralized regression function, including conditional cumulative distributionand conditional quantile functions, based on an incomplete sample $(X_t, Y_t,\zeta_t)_{t\in \mathbb{ R}^+}$ copies of a continuous-time stationary ergodicprocess $(X, Y, \zeta)$. The predictor $X$ is valued in someinfinite-dimensional space, whereas the real-valued process $Y$ is observedwhen $\zeta= 1$ and missing whenever $\zeta = 0$. Pointwise and uniformconsistency (with rates) of these estimators as well as a central limit theoremare established. Conditional bias and asymptotic quadratic error are alsoprovided. Asymptotic and bootstrap-based confidence intervals for thegeneralized regression function are also discussed. A first simulation study isperformed to compare the discrete-time to the continuous-time estimations. Asecond simulation is also conducted to discuss the selection of the optimalsampling mesh in the continuous-time case. Finally, it is worth noting that ourresults are stated under ergodic assumption without assuming any classicalmixing conditions.

Generalized regression operator estimation for continuous time functional data processes with missing at random response