scholarly journals On a (β,q)-generalized Fisher information and inequalities involvingq-Gaussian distributions

2012 ◽  
Vol 53 (6) ◽  
pp. 063303 ◽  
Author(s):  
J.-F. Bercher
Keyword(s):  
Fisher Information ◽  
Gaussian Distributions ◽  
Generalized Fisher Information

scholarly journals The Maximal Strichartz Family of Gaussian Distributions: Fisher Information, Index of Dispersion, and Stochastic Ordering

2016 ◽  
Vol 2016 ◽  
pp. 1-17
Author(s):  
Alessandro Selvitella
Keyword(s):  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Stochastic Order ◽  
Stochastic Ordering ◽  
Gaussian Distributions ◽  
Information Index ◽  
The Family ◽  
Statistical Dispersion ◽  
Fisher Information Index

We define and study several properties of what we callMaximal Strichartz Family of Gaussian Distributions. This is a subfamily of the family of Gaussian Distributions that arises naturally in the context of theLinear Schrödinger Equationand Harmonic Analysis, as the set of maximizers of certain norms introduced by Strichartz. From a statistical perspective, this family carries with itself some extrastructure with respect to the general family of Gaussian Distributions. In this paper, we analyse this extrastructure in several ways. We first compute theFisher Information Matrixof the family, then introduce some measures ofstatistical dispersion, and, finally, introduce aPartial Stochastic Orderon the family. Moreover, we indicate how these tools can be used to distinguish between distributions which belong to the family and distributions which do not. We show also that all our results are in accordance with the dispersive PDE nature of the family.

scholarly journals SEMIPARAMETRIC IDENTIFICATION AND FISHER INFORMATION

2021 ◽  
pp. 1-38
Author(s):  
Juan Carlos Escanciano
Keyword(s):  
Measurement Error ◽  
Euler Equation ◽  
Fisher Information ◽  
Systematic Approach ◽  
Statistical Information ◽  
Dimensional Parameter ◽  
Infinite Dimensional ◽  
Impossibility Results ◽  
Measures Of Risk ◽  
Generalized Fisher Information

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 the parameter is positive or zero, respectively. I first characterize these cases in models with densities linear in an infinite-dimensional parameter. I then introduce a novel “generalized Fisher information.” If positive, it implies (possibly irregular) identification when other conditions hold. If zero, it implies impossibility results on rates of estimation. Three examples illustrate the applicability of the general results. First, I consider the canonical example of average densities. Second, I show irregular identification of the median willingness to pay in contingent valuation studies. Finally, I study identification of the discount factor and average measures of risk aversion in a nonparametric Euler equation with nonparametric measurement error in consumption.

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