Entropy and the Central Limit Theorem
Copyright policy )Entropy and the Central Limit Theorem
The author establishes a strengthened central limit theorem for densities showing monotone convergence in the sense of relative entropy. The relative entropy is defined by \[ D_ n=\int f(x) \log f(x)/\phi (x)dx \] where f is the density function of a random variable, X, with finite variance and \(\phi\) is the normal density with the same mean and variance as f.
local limit theorem, 62B10, Measures of information, entropy, convolution inequalities, Fisher information, Central limit theorem, relative entropy, central limit theorem, 94A17, Central limit and other weak theorems, Statistical aspects of information-theoretic topics, 60F05, entropy
local limit theorem, 62B10, Measures of information, entropy, convolution inequalities, Fisher information, Central limit theorem, relative entropy, central limit theorem, 94A17, Central limit and other weak theorems, Statistical aspects of information-theoretic topics, 60F05, entropy
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