Print Email Facebook Twitter Functional Cramér–Rao bounds and Stein estimators in Sobolev spaces, for Brownian motion and Cox processes Title Functional Cramér–Rao bounds and Stein estimators in Sobolev spaces, for Brownian motion and Cox processes Author Musta, E. (TU Delft Statistics) Pratelli, M. (Università degli Studi di Pisa) Trevisan, D. (Università degli Studi di Pisa) Date 2017 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). Subject Cramer–Rao boundStein phenomenonMalliavin calculusCox model To reference this document use: http://resolver.tudelft.nl/uuid:7568ef6b-dbbe-4a75-9021-9dacf62a2ea8 DOI https://doi.org/10.1016/j.jmva.2016.10.011 Embargo date 2018-02-01 ISSN 0047-259X Source Journal of Multivariate Analysis, 154, 135-146 Bibliographical note Accepted Author Manuscript Part of collection Institutional Repository Document type journal article Rights © 2017 E. Musta, M. Pratelli, D. Trevisan Files PDF 8956980.pdf 418.97 KB Close viewer /islandora/object/uuid:7568ef6b-dbbe-4a75-9021-9dacf62a2ea8/datastream/OBJ/view