Estimators, escort probabilities, and phi-exponential families in statistical physics

Abstract

The lower bound of Cramer and Rao is generalized to pairs of families of probability distributions, one of which is escort to the other. This bound is optimal for certain families, called phi-exponential in the paper. Their dual structure is explored.

arXiv comment19 pages, LATEX

References in corpus (5)

• Geometry of escort distributions
• Generalized thermostatistics based on deformed exponential and logarithmic functions
• Generalized thermostatistics and mean-field theory
• Continuity of a class of entropies and relative entropies
• Euclidean and Riemannian Geometrical Approaches to Non-Extensive Thermo-Statistical Mechanics

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• Quantum Statistical Manifolds
• Stability of Evolutionary Dynamics on Time Scales
• A new class of entropic information measures, formal group theory and information geometry
• Generalized information-entropy measures and Fisher information
• Data Set Models and Exponential Families in Statistical Physics and Beyond
• Information Geometry of q-Gaussian Densities and Behaviors of Solutions to Related Diffusion Equations
• Towards an Information Geometric characterization/classification of Complex Systems. I. Use of Generalized Entropies
• Displacement convexity of generalized relative entropies
• Quantum statistical manifolds: the linear growth case
• The exponential family in abstract information theory
• Dynamics of Information Entropies in Nonextensive Systems
• Two types of $q$-Gaussian distributions used to study the diffusion in a finite region
• Cramér-Rao Lower Bounds Arising from Generalized Csiszár Divergences
• Some Information Inequalities for Statistical Inference
• Kernel Deformed Exponential Families for Sparse Continuous Attention