Non-uniform Berry-Esseen bound by unbounded exchangeable pairs approach. (English) Zbl 1488.60026
Summary: In this paper, a new technique is introduced to obtain non-uniform Berry-Esseen bounds for normal and nonnormal approximations by unbounded exchangeable pairs. This technique does not rely on the concentration inequalities developed by L. H. Y. Chen and Q.-M. Shao [Probab. Theory Relat. Fields 120, No. 2, 236–254 (2001; Zbl 0996.60029); Ann. Probab. 32, No. 3A, 1985–2028 (2004; Zbl 1048.60020)] and can be applied to the quadratic forms and the general Curie-Weiss model.
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