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Science China Mathematics

, Volume 59, Issue 12, pp 2379–2392 | Cite as

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

  • Qi-Man ShaoEmail author
  • Zhuo-Song Zhang
Articles

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.

Keywords

Stein’s method exchangeable pair limiting distribution Berry-Esseen bounds Curie-Weiss model 

MSC(2010)

60F05 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of StatisticsThe Chinese University of Hong KongHong KongChina

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