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arXiv · 1507.01494

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

Eni Musta·Maurizio Pratelli·Dario Trevisan
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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).

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Eni Musta, Maurizio Pratelli, Dario Trevisan. 2015-07-06. Functional Cramer-Rao bounds and Stein estimators in Sobolev spaces, for Brownian motion and Cox processes. https://arxiv.org/abs/1507.01494

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