Standard

Functional Cramér–Rao bounds and Stein estimators in Sobolev spaces, for Brownian motion and Cox processes. / Musta, Eni; Pratelli, M.; Trevisan, D.

In: Journal of Multivariate Analysis, Vol. 154, 2017, p. 135-146.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

Musta, E, Pratelli, M & Trevisan, D 2017, 'Functional Cramér–Rao bounds and Stein estimators in Sobolev spaces, for Brownian motion and Cox processes' Journal of Multivariate Analysis, vol. 154, pp. 135-146. https://doi.org/10.1016/j.jmva.2016.10.011

APA

Vancouver

Author

Musta, Eni ; Pratelli, M. ; Trevisan, D. / Functional Cramér–Rao bounds and Stein estimators in Sobolev spaces, for Brownian motion and Cox processes. In: Journal of Multivariate Analysis. 2017 ; Vol. 154. pp. 135-146.

BibTeX

@article{7568ef6bdbbe4a7590219dacf62a2ea8,
title = "Functional Cram{\'e}r–Rao bounds and Stein estimators in Sobolev spaces, for Brownian motion and Cox processes",
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, Cram{\'e}r–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).",
keywords = "Cramer–Rao bound, Stein phenomenon, Malliavin calculus, Cox model",
author = "Eni Musta and M. Pratelli and D. Trevisan",
note = "Accepted Author Manuscript",
year = "2017",
doi = "10.1016/j.jmva.2016.10.011",
language = "English",
volume = "154",
pages = "135--146",
journal = "Journal of Multivariate Analysis",
issn = "0047-259X",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Functional Cramér–Rao bounds and Stein estimators in Sobolev spaces, for Brownian motion and Cox processes

AU - Musta, Eni

AU - Pratelli, M.

AU - Trevisan, D.

N1 - Accepted Author Manuscript

PY - 2017

Y1 - 2017

N2 - 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).

AB - 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).

KW - Cramer–Rao bound

KW - Stein phenomenon

KW - Malliavin calculus

KW - Cox model

UR - http://resolver.tudelft.nl/uuid:7568ef6b-dbbe-4a75-9021-9dacf62a2ea8

U2 - 10.1016/j.jmva.2016.10.011

DO - 10.1016/j.jmva.2016.10.011

M3 - Article

VL - 154

SP - 135

EP - 146

JO - Journal of Multivariate Analysis

T2 - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

ER -

ID: 8956980