Necessary and sufficient conditions for the asymptotic normality of perturbed sample quantiles

DOI10.1016/0378-3758(93)90067-GzbMath0817.62010OpenAlexW1997819568MaRDI QIDQ2365867

Shan Sun, Stefan S. Ralescu

Publication date: 29 June 1993

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-3758(93)90067-g

zbMATH Keywords

asymptotic normalitycentral limit theoremkernel estimatecumulative distributionperturbed sample quantilessequence of window-width

Mathematics Subject Classification ID

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

Related Items (14)

The asymptotic law of the local oscillation modulus of the empirical process ⋮ Berry-Esséen rate in asymptotic normality for perturbed sample quantiles ⋮ Perturbed empirical distribution functions and quantiles under dependence ⋮ Smooth estimate of quantiles under association ⋮ Characterization of weak convergence for smoothed empirical and quantile processes under \(\varphi\)-mixing ⋮ Bootstrap variance estimation for Nadaraya quantile estimator ⋮ Kernel type smoothed quantile estimation under long memory ⋮ Unnamed Item ⋮ A remainder estimate for the normal approximation of perturbed sample quantiles ⋮ Some Asymptotic Properties Between Smooth Empirical and Quantile Processes for Dependent Random Variables ⋮ Asymptotic deviations between perturbed empirical and quantile processes ⋮ Quantile regression without the curse of unsmoothness ⋮ Smooth quantile estimators under strong mixing: necessary and sufficient conditions on bandwidth for weak convergence ⋮ Quantile estimation via distribution fitting

Cites Work

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• Strong uniform consistency of integrals of density estimators
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• Nonparametric Statistical Data Modeling
• Some New Estimates for Distribution Functions
• The Asymptotic Inadmissibility of the Sample Distribution Function

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