Saddlepoint approximation for Student's \(t\)-statistic with no moment conditions

DOI10.1214/009053604000000742zbMath1068.62016arXivmath/0508604OpenAlexW1979678363MaRDI QIDQ2388339

Wang Zhou, Qui-Man Shao, Bing-Yi Jing

Publication date: 12 September 2005

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

Full work available at URL: https://arxiv.org/abs/math/0508604

zbMATH Keywords

asymptotic normalitylarge deviationEdgeworth expansionsrelative errorabsolute errorself-normalized sumStudent's \(t\)-statistic

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20)

Related Items (15)

Exact inequalities for sums of asymmetric random variables, with applications ⋮ Self-normalization: taming a wild population in a heavy-tailed world ⋮ Further refinement of self-normalized Cramér-type moderate deviations ⋮ An almost sure central limit theorem for self-normalized partial sums ⋮ Saddlepoint approximations for Studentized compound Poisson sums with no moment conditions in audit sampling ⋮ Tail probability approximations for Student's \(t\)-statistics ⋮ Tilted Edgeworth expansions for asymptotically normal vectors ⋮ Strassen-type law of the iterated logarithm for self-normalized increments of sums ⋮ Towards a universal self-normalized moderate deviation ⋮ Process convergence of self-normalized sums of i.i.d. random variables coming from domain of attraction of stable distributions ⋮ Tail approximations for the Student \(t\)-, \(F\)-, and Welch statistics for non-normal and not necessarily i.i.d. random variables ⋮ Asymptotic Expansion of the Non Null Distribution of the Two-Samplet-Statistic Under Non Normality with Application in Power Comparison ⋮ Refined self-normalized large deviations for independent random variables ⋮ Approximating the \(F\)-distribution via a general version of the modified signed log-likelihood ratio statistic ⋮ RELATIVE ERROR ACCURATE STATISTIC BASED ON NONPARAMETRIC LIKELIHOOD

Uses Software

• bootlib

Cites Work

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• Edgeworth expansion for Student's t statistic under minimal moment conditions
• Some extensions of the LIL via self-normalizations
• Self-normalized laws of the iterated logarithm
• Self-normalized large deviations
• When is the Student \(t\)-statistic asymptotically standard normal?
• An exponential nonuniform Berry-Esseen bound for self-normalized sums
• Saddlepoint methods and statistical inference. With comments and a rejoinder by the author
• Limit distributions of self-normalized sums
• Saddle point approximation for the distribution of the sum of independent random variables
• Series approximation methods in statistics.

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