  We investigate the problems of drift estimation for a shifted Brownian motion
and intensity estimation for a Cox process on a finite interval $[0,T]$, when
the risk is given by the energy functional associated to some fractional
Sobolev space $H^1_0\subset W^{\alpha,2}\subset L^2$. In both situations,
Cramer-Rao lower bounds are obtained, entailing in particular that no unbiased
estimators with finite risk in $H^1_0$ exist. By Malliavin calculus techniques,
we also study super-efficient Stein type estimators (in the Gaussian case).
