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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>>