Calculus of Variations and Geometric Measure Theory

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



Inserted: 10 jun 2017

Year: 2015

ArXiv: 1507.01494 PDF


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).