On the self-normalized Cramér-type large deviation

DOI10.1007/s10959-005-7531-5zbMath1087.60026OpenAlexW2008368055MaRDI QIDQ2576805

John Robinson, Qiying Wang

Publication date: 14 December 2005

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

Full work available at URL: https://doi.org/10.1007/s10959-005-7531-5

zbMATH Keywords

domain of attraction of the normal lawstudentized meanCramér-Esseen bound

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Large deviations (60F10)

Related Items (10)

Self-normalization: taming a wild population in a heavy-tailed world ⋮ Further refinement of self-normalized Cramér-type moderate deviations ⋮ Central limit theorem and near classical Berry-Esseen rate for self normalized sums in high dimensions ⋮ An almost sure central limit theorem for self-normalized weighted sums ⋮ Tilted Edgeworth expansions for asymptotically normal vectors ⋮ Refined self-normalized large deviations for independent random variables ⋮ Moderate deviations for two sample t-statistics ⋮ PITMAN MEDAL ⋮ Limit theorems for ratios of order statistics from uniform distributions ⋮ Laws of the iterated logarithm for self-normalised Lévy processes at zero

Cites Work

• Edgeworth expansion for Student's t statistic under minimal moment conditions
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• Self-normalized large deviations
• When is the Student \(t\)-statistic asymptotically standard normal?
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• Harnack inequalities for log-Sobolev functions and estimates of log-Sobolev constants
• Limit distributions of Studentized means.
• Optimal rates of convergence in the CLT for quadratic forms
• A Berry-Esséen bound for Student's statistic in the non-i. i. d. case
• Limit distributions of self-normalized sums
• On the asymptotic normality of self-normalized sums
• A Theorem on Products of Random Variables, With Application to Regression
• Moderate Deviations for Student's Statistic
• On Bounds for Moderate Deviations for Student's Statistic
• Student's t-Test Under Symmetry Conditions

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