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Cram\'er-type Moderate Deviation Theorems for Nonnormal Approximation
- Source :
- Annals of Applied Probability 2021, Vol. 31, No. 1, 247--283
- Publication Year :
- 2018
-
Abstract
- A Cram\'er-type moderate deviation theorem quantifies the relative error of the tail probability approximation. It provides theoretical justification when the limiting tail probability can be used to estimate the tail probability under study. Chen Fang and Shao (2013) obtained a general Cram\'er-type moderate result using Stein's method when the limiting was a normal distribution. In this paper, Cram\'er-type moderate deviation theorems are established for nonnormal approximation under a general Stein identity, which is satisfied via the exchangeable pair approach and Stein's coupling. In particular, a Cram\'er-type moderate deviation theorem is obtained for the general Curie--Weiss model and the imitative monomer-dimer mean-field model.<br />Comment: 49 pages
- Subjects :
- Mathematics - Probability
60F10, 60F05
Subjects
Details
- Database :
- arXiv
- Journal :
- Annals of Applied Probability 2021, Vol. 31, No. 1, 247--283
- Publication Type :
- Report
- Accession number :
- edsarx.1809.07966
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1214/20-AAP1589