Exact convergence rate and leading term in central limit theorem for Student's \(t\) statistic.

DOI10.1214/009117904000000252zbMath1060.62019arXivmath/0410148OpenAlexW2158875475MaRDI QIDQ1879831

Qiying Wang, Hall, Peter

Publication date: 15 September 2004

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0410148

zbMATH Keywords

central limit theoremStudent's statistic

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Parametric inference (62F99)

Related Items (10)

Optimal-order bounds on the rate of convergence to normality in the multivariate delta method ⋮ Exact convergence rate and leading term in central limit theorem for Student's \(t\) statistic. ⋮ Edgeworth expansions for two‐stage sampling with applications to stratified and cluster sampling ⋮ Self-normalization: taming a wild population in a heavy-tailed world ⋮ Coverage accuracy for a mean without third moment ⋮ Proof of Tomaszewski's conjecture on randomly signed sums ⋮ Shortening the distance between Edgeworth and Berry-Esseen in the classical case ⋮ Refined self-normalized large deviations for independent random variables ⋮ Jackknife method for intermediate quantiles ⋮ Malliavin Calculus and Self Normalized Sums

Cites Work

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• Edgeworth expansion for Student's t statistic under minimal moment conditions
• On the influence of extremes on the rate of convergence in the central limit theorem
• A Berry-Esseen bound for functions of independent random variables
• Convergence to a stable distribution via order statistics
• Extremal processes. II
• On the effect of random norming on the rate of convergence in the central limit theorem
• An Edgeworth expansion for symmetric statistics
• When is the Student \(t\)-statistic asymptotically standard normal?
• An exponential nonuniform Berry-Esseen bound for self-normalized sums
• Empirical Edgeworth expansions for symmetric statistics
• The Edgeworth expansion for U-statistics of degree two
• Exact convergence rate and leading term in central limit theorem for Student's \(t\) statistic.
• The Berry-Esseen bound for Student's statistic
• A Berry-Esséen bound for Student's statistic in the non-i. i. d. case
• Limit distributions of self-normalized sums
• The Berry-Esséen bound for Studentized statistics
• A Berry-Esseen bound for symmetric statistics
• On the asymptotic normality of self-normalized sums
• Asymptotic Approximations to Distributions
• The Extreme Terms of a Sample and Their Role in the Sum of Independent Variables
• Point processes, regular variation and weak convergence
• RELAXING ASSUMPTIONS IN THE ONE SAMPLE t-TEST
• The Distribution of the t-Statistic under Non-Normality
• On the Extreme Terms of a Sample From the Domain of Attraction of a Stable Law
• Second-Order and Bootstrap Approximation to Student's t-Statistic
• Student's t-Test Under Symmetry Conditions
• THE DISTRIBUTION OF ‘STUDENT'S’ t IN RANDOM SAMPLES OF ANY SIZE DRAWN FROM NON-NORMAL UNIVERSES
• SIGNIFICANCE OF DIFFERENCE BETWEEN THE MEANS OF TWO NON-NORMAL SAMPLES
• The Influence of the Maximum Term in the Addition of Independent Random Variables

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