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Berry-Esseen bounds for the chi-square distance in the Central Limit Theorem. (arXiv:1709.09410v1 [math.PR])

来源于:arXiv
The main result of this article is a Berry-Esseen-like bound, which states the convergence to the normal distribution of sums of independent, identically distributed random variables in chi-square distance, defined as the variance of the density with respect to the normal distribution. Our main assumption is that the random variables involved in the sum are independent and have polynomial density; the identical distribution hypothesis can in fact be relaxed. The method consists of taking advantage of the underlying time non-homogeneous Markovian structure and providing a Poincar{\'e}-like inequality for the non-reversible transition operator, which allows to find the optimal rate in the convergence above under matching moments assumptions. 查看全文>>