A Nonparametric Estimation Problem From Indirect Observations

This paper deals with a nonparametric estimation problem of an integral-type functional from indirect observations where the observation Yε(t) is a sum of a known function of an unobservable process Xε(t) and a Gaussian white noise, and Xε(t) is a sum of an unknown function a(t) and a Gaussian process. The minimax lower bound on the quality of nonparametric estimation is derived and an asymptotically efficient estimator is proposed. The paper concludes with some examples including one about reduction to parameter estimation.