Tail probability approximations for Student's \(t\)-statistics

DOI10.1007/s00440-005-0494-8zbMath1122.62009OpenAlexW2037611271MaRDI QIDQ2431747

Wang Zhou, Bing-Yi Jing

Publication date: 24 October 2006

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00440-005-0494-8

zbMATH Keywords

tail probabilitiesself-normalized sumslattice random variables

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Sums of independent random variables; random walks (60G50) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items (6)

Self-normalization: taming a wild population in a heavy-tailed world ⋮ An almost sure central limit theorem for self-normalized partial sums ⋮ Strassen-type law of the iterated logarithm for self-normalized increments of sums ⋮ Tail approximations for the Student \(t\)-, \(F\)-, and Welch statistics for non-normal and not necessarily i.i.d. random variables ⋮ On Large Deviations of Sums of Independent Random Variables ⋮ Refined self-normalized large deviations for independent random variables

Uses Software

• bootlib

Cites Work

• Edgeworth expansion for Student's t statistic under minimal moment conditions
• An Edgeworth expansion for symmetric statistics
• Saddlepoint methods and statistical inference. With comments and a rejoinder by the author
• Empirical Edgeworth expansions for symmetric statistics
• Saddlepoint approximation for Student's \(t\)-statistic with no moment conditions
• Saddle point approximation for the distribution of the sum of independent random variables
• Saddlepoint Approximations in Statistics
• Series approximation methods in statistics.
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