Cram\'er-type Moderate Deviation of Normal Approximation for Exchangeable Pairs
Zhang, Zhuo-Song
arXiv, Tome 2019 (2019) no. 0, / Harvested from
In Stein's method, an exchangeable pair approach is commonly used to estimate the convergence rate of normal and nonnormal approximation. Using the exchangeable pair approach, we establish a Cram\'er-type moderate deviation theorem of normal approximation for an arbitrary random variable without a bound on the difference of the exchangeable pair. A Berry--Esseen-type inequality is also obtained. The result is applied to the subgraph counts in the Erd\"os--R\'enyi random graph, local dependence, and graph dependency.
Publié le : 2019-01-28
Classification:  Mathematics - Probability,  Primary 60F10, secondary 60G60 
@article{1901.09526,
     author = {Zhang, Zhuo-Song},
     title = {Cram\'er-type Moderate Deviation of Normal Approximation for
  Exchangeable Pairs},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1901.09526}
}

Zhang, Zhuo-Song. Cram\'er-type Moderate Deviation of Normal Approximation for
  Exchangeable Pairs. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1901.09526/