Acta mathematica scientia, Series B >
RATE OF CONVERGENCE AND EXPANSION OF RÉNYI ENTROPIC CENTRAL LIMIT THEOREM
Received date: 2014-02-27
Revised date: 2014-10-13
Online published: 2015-01-20
Supported by
This work is supported by National Basic Research Program of China (973 Program) (2011CB707802, 2013CB910200) and Natural Science Foundation of China Grant (11126180).
We obtain the expansion of R´enyi divergence of order α (0 <α < 1) between the normalized sum of IID continuous random variables and the Gaussian limit under minimal moment conditions via Edgeworth-type expansion. The rate is faster than that of Shannon case, which can be used to improve the rate of convergence in total variance norm.
SUN Jian Qiang, DING Yi Ming . RATE OF CONVERGENCE AND EXPANSION OF RÉNYI ENTROPIC CENTRAL LIMIT THEOREM[J]. Acta mathematica scientia, Series B, 2015 , 35(1) : 79 -88 . DOI: 10.1016/S0252-9602(14)60140-5
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