A remainder estimate for the normal approximation of perturbed sample quantiles

DOI10.1016/0167-7152(92)90060-IzbMath0761.62020OpenAlexW2046138901MaRDI QIDQ1195576

Stefan S. Ralescu

Publication date: 14 December 1992

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-7152(92)90060-i

zbMATH Keywords

rate of convergencecentral limit theoremnormal lawnormal approximationremainder estimateBerry-Esséen type resultdistribution of the kernel- smoothed quantile estimatorperturbed empirical distributionsperturbed sample quantilesmooth statistical model

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05)

Related Items (4)

Berry-Esséen rate in asymptotic normality for perturbed sample quantiles ⋮ Berry-Esseen-type bounds for the kernel estimator of conditional distribution and conditional quantiles ⋮ Smooth estimate of quantiles under association ⋮ Asymptotic deviations between perturbed empirical and quantile processes

Cites Work

• Approximate distributions of order statistics. With applications to nonparametric statistics
• On the accuracy of the normal approximation for quantiles
• Necessary and sufficient conditions for the asymptotic normality of perturbed sample quantiles
• Remarks on Some Nonparametric Estimates of a Density Function
• Relative efficiency and deficiency of kernel type estimators of smooth distribution functions
• Improved distribution quantile estimation
• Probability Inequalities for Sums of Bounded Random Variables
• Some New Estimates for Distribution Functions
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