Cram�r type large deviations for simple linear rank statistics

DOI10.1007/BF00535723zbMath0493.60037OpenAlexW1974322577MaRDI QIDQ3956160

Wilbert C. M. Kallenberg

Publication date: 1982

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00535723

zbMATH Keywords

simple linear rank statisticsCramer type large deviation theorem

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Asymptotic distribution theory in statistics (62E20) Large deviations (60F10)

Related Items (10)

On the relative error in normal approximation for signed rank statistics with a broad range of scores ⋮ On the \(L_ p\) rates of convergence of simple linear rank statistics under contiguous alternatives ⋮ Rates of weak convergence and large deviation probabilities for linear rank tests with type I censored data ⋮ \(L_ 1\) nonuniform central limit bounds for generalized rank statistics ⋮ Rank-based max-sum tests for mutual independence of high-dimensional random vectors ⋮ \(L_ p\)-nonuniform bounds for asymptotic normality of linear rank statistics ⋮ Contiguous alternatives which preserve Cramér-type large deviations for a general class of statistics ⋮ Efficient and adaptive nonparametric test for the two-sample problem ⋮ Some asymptotic results for a broad class of nonparametric statistics ⋮ CLT-related large deviation bounds based on Stein's method

Cites Work

• Intermediate efficiency, theory and examples
• Cramer type large deviations for linear combinations of order statistics
• The rate of convergence of simple linear rank statistics under hypothesis and alternatives
• Convergence and remainder terms in linear rank statistics
• Cramér type large deviations for Studentized U-statistics
• Edgeworth expansions in nonparametric statistics
• Large Deviation Probabilities for U-Statistics
• Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives
• Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives II
• Generalization of a Probability Limit Theorem of Cramer
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