About properties of some random processes arising in the theory of statistical estimation

In the paper some conclusions about properties of statistical estimates are made on the base of analises of stochastic process realization. Particularly it is proved that the optimal equivariant plans of sequential estimation with stopping time moment $\tau$ under the conlition $E\tau=n$ are better then optimal equivariant estimates or location parameter for sample of size $n$, in the case or large values $n$. It is suggested, that density has singularities of first or second tipe.