Cramér type large deviations for Studentized U-statistics

DOI10.1007/BF01897811zbMath0617.62015OpenAlexW2091837782MaRDI QIDQ1822156

M. Vandemaele, Noël Veraverbeke

Publication date: 1985

Published in: Metrika (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/176001

zbMATH Keywords

U-statisticjackknife estimatorstandard normal distributionCramér type large devationsStudent t-statistic

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Nonparametric estimation (62G05) Central limit and other weak theorems (60F05) Large deviations (60F10)

Related Items

\(U\)-statistics in Banach spaces ⋮ Self-normalization: taming a wild population in a heavy-tailed world ⋮ Tail probability approximation for \(U\)-statistics ⋮ Cramér's type results for some bootstrapped \(U\)-statistics ⋮ Some asymptotic results for a broad class of nonparametric statistics ⋮ Cramér type moderate deviation theorems for self-normalized processes ⋮ [https://portal.mardi4nfdi.de/wiki/Publication:3956160 Cram�r type large deviations for simple linear rank statistics]

Cites Work

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• The order of the normal approximation for a Studentized U-statistic
• Cramer type large deviations for linear combinations of order statistics
• The Berry-Esseen theorem for U-statistics
• Edgeworth expansions in nonparametric statistics
• Limit Theorems for Sums of Independent Variables Taking into Account Large Deviations. I
• Large Deviation Probabilities for U-Statistics
• Jackknifing $U$-Statistics
• A Class of Statistics with Asymptotically Normal Distribution

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