The University of Southampton
University of Southampton Institutional Repository

A Cramér Rao bound for point processes

A Cramér Rao bound for point processes
A Cramér Rao bound for point processes
The Cramér Rao bound provides a minimum achievable variance or covariance for a parameter for a univariate or vector-valued parameter. Point processes often have parameters that are described by functions and the variance and covariance for point processes are themselves functions with spatial variates. Consequently, the usual formulation of the Cramér Rao bound in these contexts is not applicable. The second-order derivative of Kullback's inequality, which relates the Kullback-Leibler divergence to Cramér's rate function, provides a description of the Cramér Rao bound. We follow this approach to develop a form of Cramér Rao bound for point processes and random measures derived from the second-order functional derivative of Kullback's inequality, which relates the Kullback-Leibler divergence to Cramér's rate functional for point processes and random measures.
Cramér Rao bound, Cramér's rate functional, effective action, Fisher information, Kullback's inequality, point processes, random measures
0018-9448
2147-2155
Clark, Daniel E.
537f80e8-cbe6-41eb-b1d4-31af1f0e6393
Clark, Daniel E.
537f80e8-cbe6-41eb-b1d4-31af1f0e6393

Clark, Daniel E. (2022) A Cramér Rao bound for point processes. IEEE Transactions on Information Theory, 68 (4), 2147-2155. (doi:10.1109/TIT.2022.3140374).

Record type: Article

Abstract

The Cramér Rao bound provides a minimum achievable variance or covariance for a parameter for a univariate or vector-valued parameter. Point processes often have parameters that are described by functions and the variance and covariance for point processes are themselves functions with spatial variates. Consequently, the usual formulation of the Cramér Rao bound in these contexts is not applicable. The second-order derivative of Kullback's inequality, which relates the Kullback-Leibler divergence to Cramér's rate function, provides a description of the Cramér Rao bound. We follow this approach to develop a form of Cramér Rao bound for point processes and random measures derived from the second-order functional derivative of Kullback's inequality, which relates the Kullback-Leibler divergence to Cramér's rate functional for point processes and random measures.

This record has no associated files available for download.

More information

Published date: 1 April 2022
Additional Information: Funding Information: This work was supported by the Joint Air Force Research Laboratory-Defence Science and Technology Laboratory (AFRLDstl) Basic-Research Grant in Autonomous Signal Processing through the Air Force Office of Scientific Research (AFOSR) under Grant FA9550-19-1-7008 and through Dstl Task under Grant 1000133068. Publisher Copyright: © 1963-2012 IEEE.
Keywords: Cramér Rao bound, Cramér's rate functional, effective action, Fisher information, Kullback's inequality, point processes, random measures

Identifiers

Local EPrints ID: 475485
URI: http://eprints.soton.ac.uk/id/eprint/475485
ISSN: 0018-9448
PURE UUID: 7ed27d0b-e368-4525-987e-4acc124aea00

Catalogue record

Date deposited: 20 Mar 2023 17:41
Last modified: 17 Mar 2024 13:11

Export record

Altmetrics

Contributors

Author: Daniel E. Clark

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×