Abstract:
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.
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