Fisher information and the central limit theorem
نویسندگان
چکیده
منابع مشابه
Fisher information and the central limit theorem
An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is studied via properties of the Fisher information along convolutions.
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A new information-theoretic approach to the central limit theorem for stable laws is presented. The main novelty is the concept of relative fractional Fisher information, which shares most of the properties of the classical one, included Blachman-Stam type inequalities. These inequalities relate the fractional Fisher information of the sum of n independent random variables to the information co...
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We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L2 spaces and Poincaré inequalities, to provide a better understanding of the decrease in Fisher Information implied by results of Barron and Brown. We show that if the standardized Fisher Information ever becomes finite then it conver...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2013
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-013-0500-5