Non-uniform bounds and Edgeworth expansions in self-normalized limit theorems

DOI10.1007/S10959-024-01376-8MaRDI QIDQ6633636

Publication date: 6 November 2024

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

entropy rate of convergence central limit theorem Edgeworth expansion local limit theorem self-normalized sums total variation distance non-uniform bounds student \(t\)-statistic

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Strong limit theorems (60F15)

Cites Work

Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Linear functional analysis. An application-oriented introduction. Translated from the 6th German edition by Robert Nürnberg
Rate of convergence and Edgeworth-type expansion in the entropic central limit theorem
Self-normalized limit theorems: a survey
Edgeworth expansion for Student's t statistic under minimal moment conditions
Edgeworth expansions and rates of convergence for normalized sums: Chung's 1946 method revisited
Non-uniform bounds in local limit theorems in case of fractional moments. I
Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates
Regularly varying rates of decrease for moduli of continuity and Fourier transforms of functions on \({\mathbb{R}}^ d\)
The entropic Erdős-Kac limit theorem
Entropy and the central limit theorem
Bootstrap procedures under some non-i.i.d. models
A Berry-Esseen bound for functions of independent random variables
On moment conditions for valid formal Edgeworth expansions
On the asymptotic accuracy of Efron's bootstrap
Edgeworth expansion of a function of sample means
On the validity of the formal Edgeworth expansion
On the effect of random norming on the rate of convergence in the central limit theorem
Exchangeably weighted bootstraps of the general empirical process
The weighted bootstrap
An Edgeworth expansion for symmetric statistics
When is the Student \(t\)-statistic asymptotically standard normal?
Self-normalized Cramér-type large deviations for independent random variables.
An exponential nonuniform Berry-Esseen bound for self-normalized sums
Rényi divergence and the central limit theorem
Empirical Edgeworth expansions for symmetric statistics
Exact convergence rate and leading term in central limit theorem for Student's \(t\) statistic.
Limit distributions of Studentized means.
The Berry-Esseen bound for Student's statistic
New Edgeworth-type expansions with finite sample guarantees
Edgeworth approximations for distributions of symmetric statistics
Asymptotic behavior of Rényi entropy in the central limit theorem
Nonclassical Berry-Esseen inequalities and accuracy of the bootstrap
Fisher information and the central limit theorem
Bootstrap and wild bootstrap for high dimensional linear models
Saddlepoint approximation for Student's \(t\)-statistic with no moment conditions
On the self-normalized Cramér-type large deviation
One term Edgeworth expansion for Student's \(t\) statistic
Measures, Integrals and Martingales
A Berry-Esseen bound for symmetric statistics
Second-Order and Bootstrap Approximation to Student's t-Statistic
Moderate Deviations for Student's Statistic
A survey of the theory of characteristic functions
The Approximate Distribution of Student's Statistic
The bootstrap and Edgeworth expansion

This page was built for publication: Non-uniform bounds and Edgeworth expansions in self-normalized limit theorems

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6633636)