A differential for L-statistics

DOI10.1214/aos/1176344781zbMath0423.62021OpenAlexW1968433015MaRDI QIDQ1134464

Dennis D. Boos

Publication date: 1979

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

Full work available at URL: https://doi.org/10.1214/aos/1176344781

zbMATH Keywords

asymptotic normalitylaw of iterated logarithmL-statisticslinear combinations of order statisticsFrechet-type differential

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Order statistics; empirical distribution functions (62G30) Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Abstract differentiation theory, differentiation of set functions (28A15)

Related Items (27)

Rates of convergence for the distance between distribution function estimators ⋮ Asymptotic normality of linear functions of concomitants of order statistics ⋮ Information bounds for nonparametric estimators of \(L\)-functionals and survival functionals under censored data ⋮ Asymptotic results in robust quasi-Bayesian estimation ⋮ Central limit theorems under alternatives for a broad class of nonparametric statistics ⋮ On a non-monotonic ageing class based on the failure rate average ⋮ Estimating L-functionals for heavy-tailed distributions and application ⋮ Asymptotic representation of m-estimators and rate of convergence of one-step m-estimators for parametric models with shrinking contamination ⋮ Almost sure representations of weightedU-statistics with applications ⋮ Necessary and sufficient conditions for asymptotic normality of trimmed L-statistics ⋮ The effects on convergence of substituting parameter estimates into U- statistics and other families of statistics ⋮ Tests for properties of residual life ⋮ Some asymptotic results for a broad class of nonparametric statistics ⋮ Multivariate trimmed means based on the Tukey depth ⋮ Delta method in large deviations and moderate deviations for estimators ⋮ Consistency of jackknife variance estimators jun ⋮ Income inequality measures based on sample surveys ⋮ Estimators of Influence Function ⋮ Functional calculus and asymptotic theory for statistical analysis ⋮ Differentiability of \(t\)-functionals of location and scatter ⋮ Exact and asymptotic tests of exponentiality against nonmonotonic mean time to failure type alternatives ⋮ Detecting trend change in hazard functions -- an \(L\)-statistic approach ⋮ On the invariance principle for differentiable statistical functionals ⋮ A robust principal component analysis ⋮ Tests for properties of the percentile residual life function ⋮ Cramér-von Mises statistics based on the sample quantile function and estimated parameters ⋮ Asymptotic distribution theory of statistical functionals: The compact derivative approach for robust estimators

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