Strong limit theorems for weighted quantile processes

DOI10.1214/aop/1176991588zbMath0659.60052OpenAlexW2050225189MaRDI QIDQ1112439

David M. Mason, John H. J. Einmahl

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1214/aop/1176991588

zbMATH Keywords

Wiener processesrelative compactnessfunctional law of the iterated logarithmBrownian bridgesweighted uniform empirical processesalmost sure behaviour of weighted uniform quantile processesStrong approximationstruncated quantile process

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)

Related Items (20)

Weighted uniform consistency of kernel density estimators. ⋮ On the relationship between the almost sure stability of weighted empirical distributions and sums of order statistics ⋮ A Strong Invariance Theorem of the Tail Empirical Copula Processes ⋮ The almost sure behavior of the oscillation modulus of the multivariate empirical process ⋮ A nonparametric sequential test with power 1 for the mean of Lévy-stable laws with infinite variance ⋮ Approximation of high quantiles from intermediate quantiles ⋮ Strong laws for local quantile processes ⋮ Return level bounds for discrete and continuous random variables ⋮ Tail inverse regression: dimension reduction for prediction of extremes ⋮ Bootstrap approximation of tail dependence function ⋮ A functional law of the iterated logarithm for tail quantile processes ⋮ Limit theorems for tail processes with application to intermediate quantile estimation ⋮ Nonstandard strong laws for local quantile processes ⋮ Asymptotic distribution and simultaneous confidence bands for ratios of quantile functions ⋮ Weighted least squares estimation of the extreme value index ⋮ Tail expectile process and risk assessment ⋮ Existence and consistency of the maximum likelihood estimator for the extreme value index ⋮ Limit theorems for the negative parts of weighted multivariate empirical processes with application ⋮ Asymptotics of an empirical bridge of regression on induced order statistics ⋮ A functional law of the iterated logarithm for kernel-type estimators of the tail index

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