A generalization of Chentsov's projection estimates

In 1962, N. N. Chentsov suggested the following method of estimation a functional parameter $\theta$ belonging to a Hilbert space $H$. He suggested to project $\theta$ on finite-dimensional subspaces of $H$ and consider as estimates of $\theta$ estimates of these projections. In this paper, we suggest to consider the projections on all reproducing kernel subspaces of $H$.