Cramér-type moderate deviation of normal approximation for unbounded exchangeable pairs

Abstract: In Stein's method, the exchangeable pair approach is commonly used to estimate the approximation errors in normal approximation. In this paper, we establish a Cram\'er-type moderate deviation theorem of normal approximation for unbounded exchangeable pairs. As applications, Cram\'er-type moderate deviation theorems for the sums of local statistics and general Curie--Weiss model are obtained.