## E. Musta - M. Pratelli - D. Trevisan

# Functional Cramer-Rao bounds and Stein estimators in Sobolev spaces, for
Brownian motion and Cox processes

created by trevisan on 10 Jun 2017

[

BibTeX]

*preprint*

**Inserted:** 10 jun 2017

**Year:** 2015

**Abstract:**

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).