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

Journal article (2017)

Authors

E. Musta Statistics - EEMCS
M. Pratelli Università degli Studi di Pisa
D. Trevisan Università degli Studi di Pisa
Research Group
Statistics (EEMCS) (TU Delft)
Copyright: © 2017 E. Musta, M. Pratelli, D. Trevisan
DOI: https://doi.org/10.1016/j.jmva.2016.10.011
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Published Date

2017

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Statistics

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 .
In both situations, Cramér–Rao lower bounds are obtained, entailing in
particular that no unbiased estimators (not necessarily adapted) with
finite risk in exist. By Malliavin calculus techniques, we also study super-efficient Stein type estimators (in the Gaussian case).

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