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This paper deals with Cram\'er-Rao inequalities in the context of nonextensive statistics and in estimation theory. It gives characterizations of generalized q-Gaussian distributions, and introduces generalized versions of Fisher…

Mathematical Physics · Physics 2012-06-05 J. -F. Bercher

Structured optical beams possess rich spatial features that are commonly characterized using entropic measures of field complexity. However, such measures do not directly quantify the operational usefulness of optical structure for…

Optics · Physics 2025-12-30 J. Sumaya-Martinez , J. Mulia-Rodriguez

The importance of the quantum Fisher information metric is testified by the number of applications that this has in very different fields, ranging from hypothesis testing to metrology, passing through thermodynamics. Still, from the rich…

Quantum Physics · Physics 2024-04-30 Matteo Scandi , Paolo Abiuso , Jacopo Surace , Dario De Santis

We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary…

Probability · Mathematics 2013-04-05 Christophe Ley , Yvik Swan

The goal of this work is to introduce and investigate a generalised Fisher Information in the setting of linear Fokker-Planck equations. This functional, which depends on two functions instead of one, exhibits the same decay behaviour as…

Analysis of PDEs · Mathematics 2026-02-11 Anton Arnold , Amit Einav , Tobias Wöhrer

The concept of Fisher information can be useful even in cases where the probability distributions of interest are not absolutely continuous with respect to the natural reference measure on the underlying space. Practical examples where this…

Statistics Theory · Mathematics 2018-03-28 Jeremie Houssineau , Ajay Jasra , Sumeetpal S. Singh

The Fisher information matrix is a quantity of fundamental importance for information geometry and asymptotic statistics. In practice, it is widely used to quickly estimate the expected information available in a data set and guide…

Methodology · Statistics 2023-06-06 William R. Coulton , Benjamin D. Wandelt

The convergence to stable laws is studied in relative Fisher information for sums of i.i.d. random variables.

Probability · Mathematics 2014-07-07 S. G. Bobkov , G. P. Chistyakov , F. Götze

In this contribution, quantum Fisher information is utilized to estimate the parameters of a central qubit interacting with a single-spin qubit. The effect of the longitudinal, transverse and the rotating strengths of the magnetic field on…

Quantum Physics · Physics 2018-04-04 N. Metwally

In this chapter, a statistical measure of complexity and the Fisher-Shannon information product are introduced and their properties are discussed. These measures are based on the interplay between the Shannon information, or a function of…

Chaotic Dynamics · Physics 2012-01-13 Ricardo Lopez-Ruiz , Jaime Sanudo , Elvira Romera , Xavier Calbet

We present a novel synthesis of Fisher information and asset pricing theory that yields a practical method for reconstructing the probability density implicit in security prices. The Fisher information approach to these inverse problems…

Statistical Mechanics · Physics 2008-12-10 Raymond J. Hawkins , B. Roy Frieden

Many statistical models require an estimation of unknown (co)-variance parameter(s) in a model. The estimation usually obtained by maximizing a log-likelihood which involves log determinant terms. In principle, one requires the…

Computation · Statistics 2016-09-05 Shengxin Zhu , Tongxiang Gu , Xiaowen Xu , Zeyao Mo

In this era of Big Data, proficient use of data mining is the key to capture useful information from any dataset. As numerous data mining techniques make use of information theory concepts, in this paper, we discuss how Fisher information…

Information Theory · Computer Science 2016-11-17 Nasir Ahmad , Sybil Derrible , Tarsha Eason , Heriberto Cabezas

We show that both the classical as well as the quantum definitions of the Fisher information faithfully identify resourceful quantum states in general quantum resource theories, in the sense that they can always distinguish between states…

Quantum Physics · Physics 2021-11-25 Kok Chuan Tan , Varun Narasimhachar , Bartosz Regula

The Fisher information matrix summarizes the amount of information in a set of data relative to the quantities of interest. There are many applications of the information matrix in statistical modeling, system identification and parameter…

Computation · Statistics 2014-05-08 Xumeng Cao

This paper provides a systematic approach to semiparametric identification that is based on statistical information as a measure of its "quality". Identification can be regular or irregular, depending on whether the Fisher information for…

Statistics Theory · Mathematics 2021-07-01 Juan Carlos Escanciano

A relationship between the Fisher information and the characteristic function is established with the help of two inequalities. A necessary and sufficient condition for equality is found. These results are used to determine the asymptotic…

Information Theory · Computer Science 2010-07-12 Cihan Tepedelenlioglu , Mahesh K. Banavar , Andreas Spanias

The Fisher information of the classical orthogonal polynomials with respect to a parameter is introduced, its interest justified and its explicit expression for the Jacobi, Laguerre, Gegenbauer and Grosjean polynomials found.

Classical Analysis and ODEs · Mathematics 2007-05-23 J. S. Dehesa , B. Olmos , R. J. Yanez

We propose a modified $\chi^{\beta}$-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cram\'er-Rao inequalities, involving this Fisher information,…

Information Theory · Computer Science 2013-05-28 Jean-François Bercher

Fisher information measures a disorder system, which is specified by a corresponding probability, the likelihood. In this article, we provide a bridge to connect classical and quantum mechanics by using Fisher information. Following the…

Quantum Physics · Physics 2014-12-30 Tzu-Chao Hung