Entropy inequalities and the Central Limit Theorem

Oliver Johnson

Stochastic Processes and their Applications, 2000, vol. 88, issue 2, 291-304

Abstract: Motivated by Barron (1986, Ann. Probab. 14, 336-342), Brown (1982, Statistics and Probability: Essays in Honour of C.R. Rao, pp. 141-148) and Carlen and Soffer (1991, Comm. Math. Phys. 140, 339-371), we prove a version of the Lindeberg-Feller Theorem, showing normal convergence of the normalised sum of independent, not necessarily identically distributed random variables, under standard conditions. We give a sufficient condition for convergence in the relative entropy sense of Kullback-Leibler, which is strictly stronger than L1. In the IID case we recover the main result of Barron [1].

Keywords: Normal; convergence; Entropy; Fisher; Information (search for similar items in EconPapers)
Date: 2000
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