On Nonparametric Estimation of a Linear Functional of the Regression Function in Observation Planning

We construct an asymptotically optimal observation plan and a corresponding asymptotically efficient nonparametric estimator of a linear functional of the regression function under various assumptions about the observation noise. This estimation plan is asymptotically best both when we have very poor prior (compactness) information about the regression function as well as when sufficiently detailed information is available and the function is smooth.