Self-normalized Cramér type moderate deviations for martingales and applications
type: Item
instance of: scholarly article
title: Self-normalized Cramér type moderate deviations for martingales and applications
author: Xiequan Fan
author: Q. M. Shao
published in: Bernoulli
publication date: 2024-11-05T00:00:00Z
review text: The authors establish self-normalized Cramér type moderate deviations for martingales under some mild conditions. \N\NCramér's moderate deviations give a quantitative estimate for the relative error of the normal approximation and provide theoretical justifications for many estimators used in statistics.\N\NApplications of the result to Student's statistic, stationary martingale difference sequences and branching processes in a random environment are discussed.
reviewed by: Pavel Stoynov
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 7938562
zbMATH Keywords: branching process in a random environment
zbMATH Keywords: Cramér's moderate deviations
zbMATH Keywords: martingales
zbMATH Keywords: self-normalized sequences
zbMATH Keywords: Student's statistic
MaRDI profile type: Publication
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DOI: 10.3150/24-BEJ1722
description: scientific article; zbMATH DE number 7938562