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).
Original language | English |
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Pages (from-to) | 135-146 |
Number of pages | 12 |
Journal | Journal of Multivariate Analysis |
Volume | 154 |
DOIs | |
Publication status | Published - 2017 |
Bibliographical note
Accepted Author ManuscriptKeywords
- Cramer–Rao bound
- Stein phenomenon
- Malliavin calculus
- Cox model