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Identifying the limiting distribution by a general approach of Stein’s method

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Abstract

A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximation is also studied. In particular, a Berry-Esseen type bound of O(n −3/4) is obtained for the Curie-Weiss model at the critical temperature.

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Correspondence to Qi-Man Shao.

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In memory of Professor Xiru Chen (1934–2005)

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Shao, QM., Zhang, ZS. Identifying the limiting distribution by a general approach of Stein’s method. Sci. China Math. 59, 2379–2392 (2016). https://doi.org/10.1007/s11425-016-0322-3

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