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

Eni Musta, M. Pratelli, D. Trevisan

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
13 Downloads (Pure)

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 languageEnglish
Pages (from-to)135-146
Number of pages12
JournalJournal of Multivariate Analysis
Volume154
DOIs
Publication statusPublished - 2017

Keywords

  • Cramer–Rao bound
  • Stein phenomenon
  • Malliavin calculus
  • Cox model

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