On estimation of functions of a parameter observed in Gaussian noise

The main problem of the paper looks as follows. A functional parameter $\theta\in\Theta\subset L_2(-\infty,\infty)$ is observed in Gaussian noise. The problem is to estimate the value $F(\theta)$ of a given function $F$. A construction of asymptotically efficient estimates for $F(\theta)$ is suggested under the conditions that $\Theta$ admits approximations by subspaces $H_T\subset L_2$ with the reproducing kernels $K_T(t, s)$, $K_T(t,t)\le T$.