Necessary and sufficient conditions for asymptotic normality of \(L\)- statistics

DOI10.1214/aop/1176989529zbMath0765.62024OpenAlexW2086890431MaRDI QIDQ1203656

David M. Mason, Galen R. Shorack

Publication date: 22 February 1993

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

Full work available at URL: https://doi.org/10.1214/aop/1176989529

zbMATH Keywords

order statisticsasymptotic normalityregular variationrepresentation formulastochastic compactnessdomain of attraction of the normal distributiongeneral \(L\)-statisticpossible subsequential limit laws

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Order statistics; empirical distribution functions (62G30)

Related Items (15)

Information bounds for nonparametric estimators of \(L\)-functionals and survival functionals under censored data ⋮ Uniform CLT, WLLN, LIL and bootstrapping in a data analytic approach to trimmed \(L\)-statistics ⋮ Estimating L-functionals for heavy-tailed distributions and application ⋮ Asymptotic distributions for a class of generalized \(L\)-statistics ⋮ Necessary and sufficient conditions for asymptotic normality of trimmed L-statistics ⋮ Moderate deviations for a class of L-statistics ⋮ The law of the iterated logarithm and central limit theorem for \(L\)-statistics ⋮ Berry–Esseen Bound for a Class of NormalizedL-Statistics ⋮ Hermite expansion and estimation of monotonic transformations of Gaussian data ⋮ Nonparametric prediction of future order statistics ⋮ Linear rank statistics, finite sampling, permutation tests and Winsorizing ⋮ Sharp large deviations for a class of normalized L-statistics and applications ⋮ On asymptotic linearity of L-estimates ⋮ Asymptotic distributions of linear combinations of intermediate order statistics ⋮ An exponential nonuniform convergence rate for a class of normalized L-statistics

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