A law of the logarithm for kernel quantile density estimators

DOI10.1214/aop/1176988741zbMath0805.60024OpenAlexW2067204755MaRDI QIDQ1336578

Xiaojing Xiang

Publication date: 29 January 1995

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

Full work available at URL: https://doi.org/10.1214/aop/1176988741

zbMATH Keywords

optimal bandwidthsKaplan-Meier estimatorstrong Gaussian approximationoscillation modulusalmost sure uniform convergencekernel-type quantile density estimators

Mathematics Subject Classification ID

Nonparametric estimation (62G05) Order statistics; empirical distribution functions (62G30) Strong limit theorems (60F15)

Related Items (11)

Uniform consistency of generalized kernel estimators of quantile density ⋮ On pointwise laws of iterated logarithm for estimators of certain conditional functionals ⋮ Tail exponent estimation via broadband log density-quantile regression ⋮ Nonparametric estimation of quantile density function for truncated and censored data ⋮ Sequential confidence bands for quantile densities under truncated and censored data ⋮ Nonparametric estimation of hazard quantile function ⋮ Nonparametric likelihood ratio confidence bands for quantile functions from incomplete survival data ⋮ A Berry-Esseen-type theorem of quantile density estimators ⋮ New Entropy Estimator with an Application to Test of Normality ⋮ A strong representation of the product-limit estimator for left truncated and right censored data ⋮ Almost-sure uniform error bounds of general smooth estimators of quantile density functions.

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