Eni Musta

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

We investigate the problems of drift estimation for a shifted Brownian motion and intensity estimation for a Cox process on a finite interval

Smooth estimation of a monotone hazard and a monotone density under random censoring

[0,T]

Isotonized smooth estimators of a monotone baseline hazard in the Cox model

, when the risk is given by the energy functional associated to some fractional Sobolev space

Estimation of the marginal expected shortfall under asymptotic independence

H^1_0\subset W^{\alpha,2}\subset L^2

A central limit theorem for the Hellinger loss of Grenander type estimators

. In both situations, Cramer-Rao lower bounds are obtained, entailing in particular that no unbiased estimators with finite risk in

Central limit theorems for the

H^1_0

L_p

exist. By Malliavin calculus techniques, we also study super-efficient Stein type estimators (in the Gaussian case).