Estimation in white Gaussian noise by means of finite number of linear statistics

We consider the asymptotical properties of estimators $T$, which are measurable in respect to statistics
$$ Y_i=\int_0^1 \psi_i(t)\,dX_\varepsilon(t) $$
if the observed process $X_\varepsilon(t)$ is determined by (1). The problem is to find the best «filters» $\psi_1(t),\dots,\psi_N(t)$ for subsequent estimation of $\theta$.
It is proved that the best in minimax sense are the functions $\psi_i$ which determine the $N$-dimensional projector on the subspace, which is the tightest one to $\partial S/\partial\theta$ in some sense. More precisely it is necessary to consider the tightest projector among the admissible (in the sense of (11)) projectors. The examples, for which the optimal filters $\psi_i$ can be found, are considered.