A note on limit theorems for perturbed empirical processes

DOI10.1016/0304-4149(89)90073-2zbMath0684.60005OpenAlexW2017445417MaRDI QIDQ1825502

Joseph E. Yukich

Publication date: 1989

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(89)90073-2

zbMATH Keywords

invariance principleslaws of large numbersperturbed empirical distribution functions

Mathematics Subject Classification ID

Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (10)

Necessary and sufficient conditions for the asymptotic normality of perturbed sample quantiles ⋮ Perturbed empirical distribution functions and quantiles under dependence ⋮ Nonparametric recursive method for moment generating function kernel-type estimators ⋮ Boundary-free kernel-smoothed goodness-of-fit tests for data on general interval ⋮ On the smoothed bootstrap ⋮ Some Asymptotic Properties Between Smooth Empirical and Quantile Processes for Dependent Random Variables ⋮ Chung--Smirnov property for perturbed empirical distribution functions ⋮ A note on the strong approximation of the smoothed empirical process of \(\alpha\)-mixing sequences ⋮ A New Kernel Distribution Function Estimator Based on a Non‐parametric Transformation of the Data ⋮ The law of the iterated logarithm and maximal smoothing principle for the kernel distribution function estimator

Cites Work

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• Some limit theorems for empirical processes (with discussion)
• Central limit theorem for perturbed empirical distribution functions evaluated at a random point
• Donsker classes of sets
• [https://portal.mardi4nfdi.de/wiki/Publication:3322909 Sur la convergence �troite des mesures gaussiennes]
• Weak Convergence of the Empirical Characteristic Function
• Invariance principles for sums of Banach space valued random elements and empirical processes
• Strong uniform consistency of integrals of density estimators
• Convergence rate of perturbed empirical distribution functions
• Generalizations of the Glivenko-Cantelli Theorem
• On the Convergence of Empiric Distribution Functions
• Convergence of stochastic processes

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