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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Fisher information | 8/8 | https://en.wikipedia.org/wiki/Fisher_information | reference | science, encyclopedia | 2026-05-05T09:50:15.726073+00:00 | kb-cron |
Thus the Fisher information represents the curvature of the relative entropy of a conditional distribution with respect to its parameters.
== History == The Fisher information was discussed by several early statisticians, notably F. Y. Edgeworth. For example, Savage says: "In it [Fisher information], he [Fisher] was to some extent anticipated (Edgeworth 1908–9 esp. 502, 507–8, 662, 677–8, 82–5 and references he [Edgeworth] cites including Pearson and Filon 1898 [. . .])." There are a number of early historical sources and a number of reviews of this early work.
== See also == Efficiency (statistics) Observed information Fisher information metric Formation matrix Information geometry Jeffreys prior Cramér–Rao bound Minimum Fisher information Quantum Fisher information White information matrix test Other measures employed in information theory:
Entropy (information theory) Kullback–Leibler divergence Self-information
== Notes ==
== References == Cramér, Harald (1946). Mathematical methods of statistics. Princeton mathematical series. Princeton: Princeton University Press. ISBN 0-691-08004-6. {{cite book}}: ISBN / Date incompatibility (help) Edgeworth, F. Y. (Jun 1908). "On the Probable Errors of Frequency-Constants". Journal of the Royal Statistical Society. 71 (2): 381–397. doi:10.2307/2339461. JSTOR 2339461. Edgeworth, F. Y. (Sep 1908). "On the Probable Errors of Frequency-Constants (Contd.)". Journal of the Royal Statistical Society. 71 (3): 499–512. doi:10.2307/2339293. JSTOR 2339293. Edgeworth, F. Y. (Dec 1908). "On the Probable Errors of Frequency-Constants (Contd.)". Journal of the Royal Statistical Society. 71 (4): 651–678. doi:10.2307/2339378. JSTOR 2339378. Fisher, R. A. (1922-01-01). "On the mathematical foundations of theoretical statistics". Philosophical Transactions of the Royal Society of London, Series A. 222 (594–604): 309–368. Bibcode:1922RSPTA.222..309F. doi:10.1098/rsta.1922.0009. hdl:2440/15172. Frieden, B. R. (2004). Science from Fisher Information: A Unification. Cambridge Univ. Press. ISBN 0-521-00911-1. Frieden, B. Roy; Gatenby, Robert A. (2013). "Principle of maximum Fisher information from Hardy's axioms applied to statistical systems". Physical Review E. 88 (4) 042144. arXiv:1405.0007. Bibcode:2013PhRvE..88d2144F. doi:10.1103/PhysRevE.88.042144. PMC 4010149. PMID 24229152. Hald, A. (May 1999). "On the History of Maximum Likelihood in Relation to Inverse Probability and Least Squares". Statistical Science. 14 (2): 214–222. doi:10.1214/ss/1009212248. JSTOR 2676741. Hald, A. (1998). A History of Mathematical Statistics from 1750 to 1930. New York: Wiley. ISBN 978-0-471-17912-2. Lehmann, E. L.; Casella, G. (1998). Theory of Point Estimation (2nd ed.). Springer. ISBN 978-0-387-98502-2. Le Cam, Lucien (1986). Asymptotic Methods in Statistical Decision Theory. Springer-Verlag. ISBN 978-0-387-96307-5. Pratt, John W. (May 1976). "F. Y. Edgeworth and R. A. Fisher on the Efficiency of Maximum Likelihood Estimation". Annals of Statistics. 4 (3): 501–514. doi:10.1214/aos/1176343457. JSTOR 2958222. Rao, C. Radhakrishna (1945). "Information and the Accuracy Attainable in the Estimation of Statistical Parameters". Breakthroughs in Statistics. Springer Series in Statistics. Vol. 37. pp. 81–91. doi:10.1007/978-1-4612-0919-5_16. ISBN 978-0-387-94037-3. S2CID 117034671. {{cite book}}: ISBN / Date incompatibility (help); |journal= ignored (help) Savage, L. J. (May 1976). "On Rereading R. A. Fisher". Annals of Statistics. 4 (3): 441–500. doi:10.1214/aos/1176343456. JSTOR 2958221. Schervish, Mark J. (1995). Theory of Statistics. New York: Springer. ISBN 978-0-387-94546-0. Stigler, S. M. (1986). The History of Statistics: The Measurement of Uncertainty before 1900. Harvard University Press. ISBN 978-0-674-40340-6. Stigler, S. M. (1978). "Francis Ysidro Edgeworth, Statistician". Journal of the Royal Statistical Society, Series A. 141 (3): 287–322. doi:10.2307/2344804. JSTOR 2344804. Stigler, S. M. (1999). Statistics on the Table: The History of Statistical Concepts and Methods. Harvard University Press. ISBN 978-0-674-83601-3. Van Trees, H. L. (1968). Detection, Estimation, and Modulation Theory, Part I. New York: Wiley. ISBN 978-0-471-09517-0.