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
2147-2155
Clark, Daniel E.
537f80e8-cbe6-41eb-b1d4-31af1f0e6393
1 April 2022
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), .
(doi:10.1109/TIT.2022.3140374).
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.
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More information
Accepted/In Press date: 23 December 2021
e-pub ahead of print date: 4 January 2022
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
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Date deposited: 20 Mar 2023 17:41
Last modified: 17 Oct 2024 16:33
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Author:
Daniel E. Clark
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