Self-normalized moderate deviations for independent random variables

DOI10.1007/s11425-012-4527-3zbMath1260.60047OpenAlexW2013643491MaRDI QIDQ1934412

Han-Ying Liang, Wang Zhou, Bing-Yi Jing

Publication date: 28 January 2013

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-012-4527-3

zbMATH Keywords

moderate deviation\(t\)-statisticself-normalized sumincrementLIL

Mathematics Subject Classification ID

Parametric hypothesis testing (62F03) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Large deviations (60F10)

Related Items (7)

A self-normalized law of the iterated logarithm for the geometrically weighted random series ⋮ Deviation inequalities for martingales with applications ⋮ Self-normalized deviation inequalities with application to \(t\)-statistic ⋮ Sharp large deviation results for sums of independent random variables ⋮ A general result on almost sure central limit theorem for self-normalized sums for mixing sequences ⋮ Self-normalized LIL for Hanson-Russo type increments ⋮ Self-normalized Cramér type moderate deviations for martingales

Cites Work

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• An exponential nonuniform Berry-Esseen bound for self-normalized sums
• A Berry-Esséen bound for Student's statistic in the non-i. i. d. case
• A converse to the law of the iterated logarithm
• On the Probabilities of Large Deviations for Sums of Independent Random Variables

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