Central limit theorem for perturbed empirical distribution functions evaluated at a random point

DOI10.1016/0047-259X(86)90032-1zbMath0594.62056MaRDI QIDQ1077112

Stefan S. Ralescu, Madan Lal Puri

Publication date: 1986

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

central limit theoremU-statisticskernel type density estimatorperturbed empirical distribution functions

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 (11)

Necessary and sufficient conditions for the asymptotic normality of perturbed sample quantiles ⋮ Berry-Esséen rate in asymptotic normality for perturbed sample quantiles ⋮ Law of the iterated logarithm for perturbed empirical distribution functions evaluated at a random point for nonstationary random variables ⋮ On some limit laws for perturbed empirical distribution functions ⋮ Asymptotic properties of perturbed empirical distribution functions evaluated at a random point ⋮ Perturbed empirical distribution functions and quantiles under dependence ⋮ Characterization of weak convergence for smoothed empirical and quantile processes under \(\varphi\)-mixing ⋮ On the smoothed bootstrap ⋮ Central limit theorem of the smoothed empirical distribution functions for asymptotically stationary absolutely regular stochastic processes ⋮ Some Asymptotic Properties Between Smooth Empirical and Quantile Processes for Dependent Random Variables ⋮ A note on limit theorems for perturbed empirical processes

Cites Work

• On Berry-Esséen rates, a law of the iterated logarithm and an invariance principle for the proportion of the sample below the sample mean
• The oscillation behavior of empirical processes
• Remarks on Some Nonparametric Estimates of a Density Function
• Approximation Theorems of Mathematical Statistics
• Kernel density estimation revisited
• Strong uniform consistency of integrals of density estimators
• Convergence rate of perturbed empirical distribution functions
• Some New Estimates for Distribution Functions
• Sequential Confidence Intervals Based on Rank Tests
• A New Proof of the Bahadur Representation of Quantiles and an Application
• On Estimation of a Probability Density Function and Mode
• A Class of Statistics with Asymptotically Normal Distribution
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