Escort distributions minimizing the Kullback-Leibler divergence for a large deviations principle and tests of entropy level

DOI10.1007/s10463-014-0501-xzbMath1440.62033OpenAlexW2059046815MaRDI QIDQ263270

Valérie Girardin, Philippe Regnault

Publication date: 4 April 2016

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10463-014-0501-x

zbMATH Keywords

estimationlarge deviations principleKullback-Leibler divergenceinformation geometryShannon entropyescort distributionstests

Mathematics Subject Classification ID

Large deviations (60F10) Information theory (general) (94A15) Statistical aspects of information-theoretic topics (62B10)

Related Items (5)

Decision theory and large deviations for dynamical hypotheses tests: the Neyman-Pearson lemma, min-max and Bayesian tests ⋮ The conditional average entropies ⋮ Different closed-form expressions for generalized entropy rates of Markov chains ⋮ Shannon's Entropy and Its Generalisations Towards Statistical Inference in Last Seven Decades ⋮ Bayes posterior convergence for loss functions via almost additive thermodynamic formalism

Uses Software

• NIST Statistical Test Suite

Cites Work

• A Mathematical Theory of Communication
• Tsallis distribution as a standard maximum entropy solution with `tail' constraint
• An informational divergence geometry for stochastic matrices
• I-divergence geometry of probability distributions and minimization problems
• Dynamical sources in information theory: Fundamental intervals and word prefixes
• Introduction to Nonextensive Statistical Mechanics
• Limit Distributions for a Statistical Estimate of the Entropy
• Asymptotic Statistics
• Large deviations for empirical entropies ofg-measures
• On Information and Sufficiency
• Entropy-based goodness-of-fit tests—a unifying framework: Application to DNA replication
• Information Theory and Statistics: A Tutorial
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