Self-normalized Cramér type moderate deviations for stationary sequences and applications

DOI10.1016/j.spa.2020.03.001zbMath1445.60027arXiv2003.12939OpenAlexW3011700256MaRDI QIDQ2186662

Xiequan Fan, I. G. Grama, Qui-Man Shao, Quan-sheng Liu

Publication date: 9 June 2020

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.12939

zbMATH Keywords

stationary processesmoderate deviationsCramér moderate deviations

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Stationary stochastic processes (60G10) Large deviations (60F10)

Related Items (6)

Central limit theorem and self-normalized Cramér-type moderate deviation for Euler-Maruyama scheme ⋮ Self-normalized Cramér moderate deviations for a supercritical Galton–Watson process ⋮ Sharp moderate and large deviations for sample quantiles ⋮ Uniform Cramér moderate deviations and Berry-Esseen bounds for a supercritical branching process in a random environment ⋮ Cramér-type moderate deviations for the log-likelihood ratio of inhomogeneous Ornstein-Uhlenbeck processes ⋮ Cramér moderate deviations for a supercritical Galton-Watson process

Cites Work

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• Self-normalized Cramér-type moderate deviations under dependence
• Self-normalized Cramér type moderate deviations for the maximum of sums
• Self-normalized limit theorems: a survey
• Sharp large deviations for sums of bounded from above random variables
• Moderate deviations for stationary sequences of bounded random variables
• Exponential inequalities for self-normalized martingales with applications
• Moment inequalities for sums of dependent random variables under projective conditions
• Limit theorem for large deviations probabilities of certain forms
• A Cramér type large deviation result for Student's \(t\)-statistic
• On moderate deviations for martingales
• Self-normalized large deviations
• When is the Student \(t\)-statistic asymptotically standard normal?
• Donsker's theorem for self-normalized partial sums processes
• Self-normalized Cramér-type large deviations for independent random variables.
• Large deviations for martingales via Cramér's method
• A general class of exponential inequalities for martingales and ratios
• Large deviations for martingales with some applications
• Moderate deviations for martingales and mixing random processes
• A Cramér moderate deviation theorem for Hotelling's \(T^{2}\)-statistic with applications to global tests
• On necessary and sufficient conditions for the self-normalized central limit theorem
• Self-normalized Cramér type moderate deviations for martingales
• Cramér large deviation expansions for martingales under Bernstein's condition
• Large and moderate deviations for Hotelling's \(T^2\)-statistic
• On martingale approximations and the quenched weak invariance principle
• Asymptotic distribution of least squares estimators for linear models with dependent errors: regular designs
• A maximal 𝕃_{𝕡}-inequality for stationary sequences and its applications
• Self-Normalized Processes
• Nonlinear system theory: Another look at dependence
• Central limit theorems for time series regression
• The Approximate Distribution of Student's Statistic

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