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

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

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 obtain...

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Veröffentlicht in:Science China. Mathematics 2016-12, Vol.59 (12), p.2379-2392
Hauptverfasser: Shao, Qi-Man, Zhang, Zhuo-Song
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Approximation
Constraining
Critical temperature
Curie temperature
Error analysis
Exchange
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Random variables
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Zusammenfassung: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.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-016-0322-3