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Weighted Fisher informations, their derivation and use by B. Roy Frieden; Bernard H. Soffer is a Physics and Astronomy article available to read on EtoBox.
What is Weighted Fisher informations, their derivation and use about?
## Generalized Fisher information Negative Fisher information Fisher information has been used to derive many laws of physics, including its differential equations. In many of these Fisher-based derivations the information in the time measurement is required to be negative. Yet by its expression in the standard derivation of the Cramer-Rao (CR) inequality, a negative Fisher seems impossible. To the contrary, we show that in fact the standard CR derivation allows the Fisher to be meaningfully regarded as either negative or positive. The mathematics allow it, and the choice to be made depends upon the physical parameter whose information level is sought. For example, the rules of special relativity require an imaginary time parameter ict, i = √ -1, with c the speed of light and t the time. The squared time parameter is then negative, requiring (as shown) the Fisher information to be negative as well. Further generalizations of the CR derivation are also made, which allow the estimation of general parameters using arbitrarily weighted mean-squared error criteria. The weights are found to define a family of correspondingly weighted Fisher informations. Finally, a condition is found for
Who reads Weighted Fisher informations, their derivation and use?
It is typically read by researchers, students, and practitioners in Physics and Astronomy.
- Author
- B. Roy Frieden; Bernard H. Soffer
- Publisher
- Elsevier Science; Elsevier ; Elsevier BV (ISSN 0375-9601)
- Published
- 2010
- Language
- EN
- Field
- Physics and Astronomy (Physical Sciences)