Next Article in Journal
Identity Authentication over Noisy Channels
Previous Article in Journal
Informational and Causal Architecture of Discrete-Time Renewal Processes
Article Menu

Export Article

Open AccessArticle
Entropy 2015, 17(7), 4918-4939;

Fisher Information Properties

Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Monseñor Álvaro del Portillo 12.455, Las Condes, Santiago, Chile
Academic Editor: Raúl Alcaraz Martínez
Received: 18 June 2015 / Accepted: 10 July 2015 / Published: 13 July 2015
(This article belongs to the Section Information Theory, Probability and Statistics)
Full-Text   |   PDF [283 KB, uploaded 13 July 2015]


A set of Fisher information properties are presented in order to draw a parallel with similar properties of Shannon differential entropy. Already known properties are presented together with new ones, which include: (i) a generalization of mutual information for Fisher information; (ii) a new proof that Fisher information increases under conditioning; (iii) showing that Fisher information decreases in Markov chains; and (iv) bound estimation error using Fisher information. This last result is especially important, because it completes Fano’s inequality, i.e., a lower bound for estimation error, showing that Fisher information can be used to define an upper bound for this error. In this way, it is shown that Shannon’s differential entropy, which quantifies the behavior of the random variable, and the Fisher information, which quantifies the internal structure of the density function that defines the random variable, can be used to characterize the estimation error. View Full-Text
Keywords: Fisher information; Cramer–Rao bound; Shannon differential entropy; Markov chains Fisher information; Cramer–Rao bound; Shannon differential entropy; Markov chains
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Zegers, P. Fisher Information Properties. Entropy 2015, 17, 4918-4939.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top