scholarly journals Some properties of generalized Fisher information in the context of nonextensive thermostatistics

2013 ◽  
Vol 392 (15) ◽  
pp. 3140-3154 ◽  
Author(s):  
J.-F. Bercher
Keyword(s):  
Fisher Information ◽  
Generalized Fisher Information

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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