A Cramér type moderate deviation theorem for the critical Curie-Weiss model

Can, Van Hao; Pham, Viet-Hung

doi:10.1214/17-ecp96

Search citation statements

Order By: Relevance

Paper Sections

Select...

Applications1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2018

2021

Publication Types

Select...

Other1

Article1

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Alberici, Contucci and Mingione [2] showed that when (J, h) with λ c = −H (4) (m c ) > 0 and c 1 is a normalizing constant. Chen [15] obtained the Berry-Esseen bound using Stein's method.…”

Section: Applicationsmentioning

confidence: 99%

Cramér-type Moderate Deviation Theorems for Nonnormal Approximation

Shao,

Zhang,

Zhang

2018

Preprint

View full text Add to dashboard Cite

A Cramér-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 [12] obtained a general Cramér-type moderate result using Stein's method when the limiting was a normal distribution. In this paper, Cramér-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 Cramér-type moderate deviation theorem is obtained for the general Curie-Weiss model and the imitative monomer-dimer mean-field model.

show abstract

Section: Applicationsmentioning

confidence: 99%